Using mostly examples from DAA because DA2 has some Concerning “mental illness is just like ~possession~” type nonsense going on and I don’t want to wade through that. Here we go!

He's hyper empathetic. In the wending woods when he realizes people are dying for nothing and he's just so upset (his tone reminds me of how I feel whenever I watch/read Bad Things in the news), in Amaranthine he’s absolutely distraught at the thought of leaving even one person behind to die, he risked his freedom to save the life of some Bann when he was 12 years old and freshly escaped and really should have been laying low, pretty much any time someone is hurting he's literally desperate to help them

---Except when it's people who Don't Count. He has zero sympathy for Templars, even joking about the one Templar dying. And he says some pretty awful things to Fenris and Merrill, even when the latter is dealing with something horrible. He’s very black and white about this. Speaking of...

Black and white thinking. Anders is all about Good and Bad. Spirits are Good, demons are Bad. Mages are Good, Templars are Bad. Justice is Good, anger is Bad. Andraste is Good, the Chantry is Bad (he's Andrastian, but even in Awakening he approves of stealing from the Chantry and disapproves of helping it). Saving people is Good, burning a city to the ground is Bad (fun fact, Anders is the only companion who doesn’t approve of that no matter what you say. The others can be convinced. Not Anders. He can just be convinced to give in and accept it, never to agree.) 

---He sorts people he meets into Good or Bad categories too. There is no in between, although there are more extreme versions of the Good box, which are the “I know I just met you but I’m at least 50% madly in love with you” box and the “I would literally die for you, you are the definition of perfection and you can do no wrong” box). 

---Velanna: fellow mage friend, Good. Merrill: Blood mage, demons, Bad. Bethany: mage, related to Hawke, Good. Aveline: guard, married a Templar, Bad.

---I can’t think of an in game example of him splitting (going from total idealization to total  with anyone, but he absolutely would and does trust me I’m an expert. He’s absolutely the type of person who will instantly stop being friends with someone if they make fun of his cat, or if they make One insensitive joke he doesn’t like, or talk to him with the Wrong Tone.

Extreme emotions. When Anders is angry he’s ready to rip apart a half dozen Templars with his bare hands. When he’s happy there are no problems in the world and everything is perfect because he’s free and there’s pie here. (Long term plans? What do you mean long term plans? Things are fine right now?). When he’s sad (which we don’t see so much in Awakening because he’s on an up swing) he’s miserable and hopeless and hides away in his room for weeks on end because there’s literally no point to anything. When he’s in love he’s so in love. (When he’s with Karl he doesn’t even try to escape the Circle, because the Circle and all of its horrors are suddenly bearable because he has Karl. When he loves Hawke, he sees Hawke as perfect and can do no wrong, and Justice is even annoyed by this (at least at first) and sees Hawke as a distraction because Anders can’t stop thinking about them literally all the time). 

Impulsive. He is definitely impulsive. He came back to help you fight an army of darkspawn that just took out every warden and Soldier in the place because he just... wanted to help. You find him hiding around the corner from them because he was likely forced to realize he has no idea what he’s actually planning on doing. Then he agrees to join the Wardens without thinking about it at all. Then he starts a conversation with someone he barely knows by basically saying "So, Jesus is pretty fuckable, huh". The man has no filter or impulse control. 

---He impulsively overshares too. You can tell from the way he answers questions in dialogue and banter that he’d rather joke and deflect than answer personal questions honestly. And yet within like a week of meeting you he’s told you about how he’s run away from the Circle seven times and they kept him in solitary for a year once. One of the first things he says to you is that this Templar used to call him inhuman and that the Templars kick him in the head to wake him up sometimes. And you cannot convince me that any neurotypical person starts a conversation with a complete stranger with “hi, I’ve been abused for most of my life, what’s your name?”

---At least some of his Circle escapes/attempts were likely impulsive. The epilogue says he ran away from the Keep several times but came back which to me implies it’s become one of those “I feel restless and am about to do something impulsive and stupid” things

---One time when he ran away from the Circle he went to Denerim and had an orgy with a pirate

---Even joining with Justice was pretty impulsive and risky tbh. Neither of them really knew what would happen.

Anger. He’s often at least bitter and sarcastic whenever anything even slightly bad happens. If you say something that upsets him or even just reminds him of something that upsets him he either makes a sarcastic quip and gets distant and withdrawn, or he goes into a full on angry rant. Anders was super angry in DAA, and expresses it even in situations where he probably shouldn’t (snarking at the Templar who just said she wants to see him executed, at you (his boss and the only reason he’s not in the Circle or dead right now) even at the beginning when he barely knows you and can’t know how you’ll react to that, etc) like he just can’t hold it in. This anger often comes on pretty suddenly and often vanishes just as fast. 

Gets attached to people so fast. He latches onto Velanna literally as soon as you meet her (he approves of both helping her and recruiting her) and at that point all he knows about her is she’s an attractive angry elven mage who tried to use magic trees to kill you. His banters with her imply it’s at least partly if not mostly because she's a fellow mage (he wants to talk about magic with her!) Also in their banters, he’s more open with her. Nathaniel asks him how the Templars find him and he just snaps “incredibly angry, that’s how” but when Velanna asks about his escapes he tells her that they found him with his phylactery. I’m pretty sure Velanna is the only person he ever actually apologizes to for making a joke to (”(chuckes) I’m sorry, I couldn’t help myself.”). And again, she’s not even very nice to him. He’s attached to her and sees himself as closer to her even when that doesn’t seem to be reciprocated to that level. (He also does this with Hawke in DA2, where he’ll be in love with you even if you’re absolute shit to him.) 

---He gets pretty attached to the Warden-Commander pretty quickly too. 

---Anders is the "he held open a door for me once and smiled at me so now I'm planning our wedding" kind of guy, I think he’s had a bit of a crush on all of your companions at some point tbh (For sure Nate and Velanna and the Warden-Commander, and Justice, and probably Sigrun too).

---He falls in love with Hawke almost as soon as they meet too, even if you're horrible and mean to him (Hawke is his FP just saying)(I don’t mean that in a good way I mean it in an unhealthy way that he and Hawke would have to learn to talk through and fix)

Fear of abandonment, absolutely. That’s probably one of the reasons he runs from Vigil’s Keep in the epilogue. Everything’s just too good, it can’t last, something’s going to go wrong and so he might as well be the one to leave because the more he likes it there and likes the people there the worse it would be to lose it all. 

---He keeps people at a distance and acts as charming and endearing as he can, probably curses himself whenever he slips and is honest with people (which is pretty often, see impulsive oversharing) because he wants people to like him and not leave him. 

---(This is why he does the charming thing less in DA2, I think. Because he has Justice. Justice won’t leave him and Justice is always in his head thinking and believing that Anders is good whether people like him or not, and those thoughts are in Anders’ head so they’re calming these fears like subconsciously, if that makes sense?)

Lack of/unstable sense of personal identity. He has no connection to his name as seen by how he just accepted this random nickname as his name from then on, which isn't strictly a BPD thing but it is a feeling I’ve seen a lot of people with BPD relate to. 

---He doesn't really know what he wants to do because he doesn't really know who he is aside from the Circle mage who keeps escaping. If he's not the runaway mage then what is he? 

---And in DA2 he has trouble distinguishing between himself and Justice whereas Justice doesn't seem to have that problem as much (in the Fade it's always very clear when it's Justice vs Anders speaking, because Justice is in control and Justice has a better idea of who's who)

You’re definitely not the only one! I’ve heard the same from a handful of borderline people and I agree that he can easily be read that way. I think he can also be very easily read as (and I headcanon him as) having PTSD and various anxiety/panic symptoms.

YES i can totally see this

oh, and like...that would tie into his whole identity conflict wrt being a healer who is terrified of accidentally hurting innocent people.