I wrote an essay on my interpretation of Serana. I felt that it would help you guys understand my vision for my Serana Dialogue Expansion:

We can start with her life before becoming a Daughter of Coldharbour. Her father already explains much of how they began worshipping Molag Bal to begin with. They feared death and wanted to obtain immortality. They were royalty and were in control of a vast realm, so as I see it, they may have an obsession with control and thus became unable to let go of their power.

Enter Molag Bal, who can offer them what they seek but at a terrible price. Harkon already says that he sacrificed a thousand innocents, but I don't think Serana and Valerica would stand idle and get rewarded anyway. They must have been at least accomplices to some extent, so in my interpretation, Serana got her hands stained with their blood too.
So Molag Bal is pleased and is ready to reward them with immortality, but Serana learns too late that there's a catch specifically for her and her mother. You know the one. By the time she realizes, there's no turning back as her parents expect her to offer herself as Valerica states. This reveals that Serana never questioned her parents' judgement and repressed any disagreements, which means that she must have been very young when she became a Vampire and probably not mentally mature yet (late teens or early 20s). The traumatic ritual is complete and leaves a scar that will haunt her for the rest of her life, and naturally she'll avoid talking about it every time it's brought up, like any victim of that crime. And given how sheltered princesses were in medieval times, that time may have been her first…

These events have caused two traumas. The first is the obvious one, which is the root of her rejection of pursuing any relationships. I think that getting too close to a potential partner may remind her of the ritual, so she doesn't want to take the risk of reliving that even if her partner has their best intentions at heart. The second one is the sacrifices her family committed. She must have been old enough to understand what taking a life was, so, as she states in the Mod during the Dragonborn questline, she turned a blind eye to the suffering of those people (again, a thousand, make the math). Eventually she grew a conscience and began reflecting on how many lives they cut short and potentially sent to Coldharbour just so that the three of them could live forever. This causes her to feel sensitive towards acts of unnecessary cruelty, eventually evolving into a sense of justice and morality that both her parents lack. I think this is also why she can't walk into a temple in good conscience and why she believes she doesn't deserve to be happy(ly married). 

Despite all those traumas she still acts sarcastic, friendly and kinda naïve. She may not have completely healed, but she must have learned to put that aside and keep those traumas out of her mind. Think of it as a sort of a self-defense mechanism.
The way I see it, while she feels a lot of guilt and has feelings of inadequacy, she does what to be happy. That's why she tries to enjoy the moment whenever she can, especially now that she has a friend that genuinely cares about her. I know it is a bit contradictory, but human beings are contradictory when dealing with complex psychological issues like hers. On one hand she is scarred and feels that she's done too much wrongdoings to live happily, but on the other hand she craves for that joy she felt during her childhood and will subconsciously try to be that girl whenever she can, because that makes her feel safe from all the messed-up stuff that happened to her.
No one can be depressed 24/7 unless they're completely isolated, in which case it becomes a toxic vicious cycle. If they're surrounded by people who care about her, those scars can temporarily fade from her mind just by being with them. It happens with grief. You can be sad because you lost someone, but when being surrounded by your friends, that pain fades away and you can even smile simply by feeling loved and appreciated by them. So yeah, the power of friendship is real to some extent.

Then she starts living as a Vampire. I already explained why I believe she was from the 1st era in the mod page so I won't bore you with that. As she states in the vanilla game, she was closer with her mother than her father, and I believe that the distance between her and her father began after the ritual. She shows concern for him, so he must have given her reasons to love him, but then he went out of his way to offer her and his wife to the literal god of r*pe in exchange for immortality AND power, so there's no doubt in my mind that she feels betrayed and holds a grudge against him.

Her mother exploits this when the Prophecy comes into play, and as Serana states in the game, she went full divorced mom and made Serana believe that her father was a lost cause. This, after confronting her about it, becomes another source of guilt, as she believes that she could have prevented her father from becoming a monster. She yearns for the days in which they were a family. That is why the Dragonborn becomes such an important figure for her. He actually cares for her and listens to her, and in time, helps her to heal at least some of her emotional wounds. He's her first friend.
Then we add what I added with my mod. She has been living so long that some of her earliest memories just blur. I used the dog topic to show this (and admittedly could have been executed a bit better but I didn't know how) and this becomes a red flag to her, because this is exactly what happened to her father. She's afraid of losing what makes her Serana. The Dragonborn reassures her that she'll be herself as long as she keeps caring and she gets over it. In retrospective, maybe too quickly. I think this is the weakest piece of writing of the mod, which is why this concern gets brought up a little again.

After Harkon's defeat, she finds her place in the world, though in the Volkihar route, she feels that it's her responsibility to restore her clan's legacy back to it's former glory. As such, she can't be anything else. She's not against it but this traces back to how she just couldn't question her parents during her youth. Up until the Dawnguard questline, she NEVER made a decision on her own. Her arc in the vanilla game is to claim her autonomy and make her own choices, finally succeeding when she willingly opposes her father for her own reasons, not because her mother told her so. However, that is as far as she goes. Because of how she's been living all her life, she can't imagine herself being anything else than the heir to their legacy.
In the Dawnguard route, however, it's a completely different story. There's no clan to restore, so she feels lost and purposeless unless she goes adventuring with the Dragonborn. When the subject is brought up, however, Serana realizes that she is FREE. No longer bound by her parents or her clan, she can do whatever she wants and finally lead her life as she desires.

And lastly we talk about her vampirism. The game already shows that she sees it as a very important aspect of herself, as she gets offended when the player asks her if she wants to cure herself in the Prophet quest, and consequentially won't cure herself after Harkon's defeat. The way I see it, she went through too much and sacrificed too many lives to gain it, so curing herself would be rendering all that meaningless. Besides, she did get to live for many centuries, so it was worth it. But at the same time, the vampirism has deprived her of many pleasures that normal mortals possess. For starters, she is frozen in time while the world moves on and she will watch many friends pass away (the vampires of Volkihar are all psychos so they make for terrible friends). Additionally, although this isn't canon and I totally made it up, her sense of taste only reacts to blood and she can't feel warmth anymore. Lastly, there's the risk of her becoming so old that she'll lose her humanity like her father, and deep down she knows that's where she'll end up. Also, if she dies she goes to Coldharbour.
That's why curing her is a major step in her healing process. The way I see it, she's been struggling with this choice very deep down, but it isn't until her best friend encourages her to take the step when she feels ready to do it (unless they brought it up in Prophet, when they didn't have that much of confidence). In the game, after being cured, she almost speaks like someone who's gotten over their addiction. "All clean", "the world is alive, and so am I for once".

In the Skyrim main quest she doesn't get to develop much, as this is the Dragonborn's story and she's there to help, while their roles are reversed in the Dawnguard story. However, she does get to reflect on herself by the time the Dragonborn has defeated Alduin. She realizes that even the world isn't going to exist forever, and it will erode with time. This helps her come to terms with her own mortality, and stop obsessing with the future and instead savor every moment of the present. Sorry if I get emotional, but this is a conclusion I arrived myself when I lost my dog abut the same time I started writing for this mod. I didn't imagine that he would live much less than I would, so by the time he passed away I sort of realized that life isn't going to warn us when the end comes, so we have to enjoy the moment as much as we can. I'm not glad that it happened, but I'm glad that it left me a lesson that I could pass on.
Again, sorry for getting emotional, but that piece of dialogue I added at the end of the Skyrim questline felt very personal for me.

Then, in the Dragonborn questline, I already spoke of her insecurities regarding how she used to treat life and wether or not she deserves to be happy, but the second half makes her relive her Daedric worshipping days when the Dragonborn starts making deals with Hermaeus Mora, so she tries to sway them away so desperately that she becomes possessive of him, not even trying to see thing from their perspective. This brings up another layer of her character that will be further explored in my next update: whenever she fears she's going to lose someone precious, she becomes so afraid that she gets aggressive and possessive, not allowing them to make choices for themselves. This comes from the losses she has experienced, which ironically draws out the Harkon in her. Eventually she's mature enough to come around, but that fear still lingers if the Dragonborn choses to keep serving Mora. She knows where that will lead to.
Not to flatter myself, but I believe that this was a really good addition that gives her a lot of nuance. Seriously, I still can't believe that out of the three main questlines, the one from Dragonborn was the one that developed her character the most!

So, to make a long story short, Serana's arc is a story of healing, vulnerability and freedom. By the end of the quest, she has gained the courage to take control of her life and make her own decisions. In a way, is sort of a coming of age story. Maybe that's why she feels so relatable.
Oh, and as for why in my mod she feels uncomfortable when talking about her age, it's because funny haha lol XD.