She can't remember much... of what? Her past? She was taken to noblewoman's house when she was very little - it's not surprising she doesn't remember much before that. Vivienne doesn't remember her parents as well, nor she cares for them (she says her life began in a Circle)... Does that make her a goddess?
Has gift with a bow? Hardly a pointer, as I've already pointed out. All of the companions (as well as the Inquisitor) are noted to be remarkably skilled, trained or not. Besides, Sera never really answers (after she opens up) whether an initial group that accepted her into her midst also trained her - but she does say that she was given at least some pointers at the beginning, so it's not like she picked a bow and BAM! Instant master bowman.
Cole said her arrows see the mark before she even fires and she's touched by the Fade (says her ears point toward it)
Eh... I'll just re-paste what I wrote about in earlier post:
The only thing I see implied is that Sera is special, because elves are special... And I'm pretty sure it's obvious for most people now, seeing how much of the story revolves around glorious elven past, as well as the Fade to which elves have special connection to.
So, Sera is unique only in a sense that she's been raised predominantly around humans - therefore many things she thinks are weird (like, say, deja-vu) are weird for her, because she either doesn't know that it's an 'elfy thing' or nobody taught her how to react to those. It's pretty apparent in this banter (direct quote):
Sera: (shivers) Weird.
Solas: Sera? What are you feeling?
Sera: Ugh, here we go. It’s nothing, it just feels like I've seen this. Exactly this. It happens.
Solas: Not to everyone.
(If Inquisitor is an elf)
Sera: It’s not an elf thing. Inquisitor's not shaking.
(Otherwise)
Sera: It’s not an elf thing. You’re not shaking.
Neither Solas, nor elf Inquistor make a big deal out of it, because - in all likelihood - for them this is a thing they're familiar with and one they either know how to cope with or ignore, since they've been raised in a community to which it was also a familiar thing. So, to any other elf is likely just a part of life - and since they usually stick to their own, most may not even be aware that something they do is unique to themselves or worth mentioning. They live in their own, 'elfy bubble', so to speak.
It's like... it would be weird for an elf or human raised around dwarves to say that they have dreams since dwarves have no idea how is it to dream - yet among elves and humans dreaming is just part of life, therefore they don't go around being all "Uh, WEIRD!" every time it happens to them.
Also - it's a bold statement to claim that Sera has stronger connection than any other city elf, considering that there's no other city elf we spend equal time around.
There's also a tidbit in DAI that flies in the face of such assessment - easily missed, but already caught by fans, namely: after events in Temple of Mythal, if you go to Val Royeaux, you can find an elven servant there, talking about a woman calling herself Mythal in his dreams, which makes him wake up screaming every night.
And that's just a random city elf we know nothing about.
Like I said - it's more reasonable to asses that Bioware writers made Sera "special" only in a sense, that through her they've shown that elves are indeed special - even those who fervently deny any connection with their heritage, which only makes elven gifts or uniqueness of them stick out even more than they usually do.
If you look at it that way, it's actually pretty goddamn ingenious. There's no need to make it a giant (and totally unnecessary) plot twist for it to be meaningful to the story.
As for Cole making cryptic comments - he does that for everyone (thanks to that he also explains to audience how spirits and their realm works).
Plus, he also says that "he is where the knife should be", meaning that the whole 'seeing the mark before firing' think is related to some sensitivity to the Fade (Avvar warriors use similar technique) and NOT "Andruilness".
She's considered crazy and we all know Andruil went mad.
Apples and oranges... She's crazy only in a sense that she's a random goofball. Her 'craziness' can hardly be compared to Void-induced madness that made Andruil hunt for frikking gods.
Plus, how is it that people conveniently forget that Andruil has been noted to be a passionate and exceptional hunter, more than she's an archer, really? And Sera might be a good archer, but she's NOT noted to be a good hunter of any sort. In fact, she hates outdoors and gets herself lost anywhere outside of the city.
Her fear in the raw Fade is Nothing and the Void is considered that
And Iron Bull's fear is madness and - as you noted earlier - Andruil went mad. (also, if the Void was actually "nothing" would Solas say that there are 'stirrings of the energy in the Void' after his spirit friend was killed?)
"Nothing" can really mean everything - from Sera being terrified by the nothingness or silence that threatens magic and all magical creatures (and elves are ones) to irrelevance, like in case of Vivienne.
perhaps she's a chosen vessel or a key to something else
I think we have more pointers to Inquisitor being that than we do Sera.
She's not acting, she really is that way because she doesn't know who she truly is and she's very afraid she'll find out something she doesn't want to know, so she's always in denial.
Yet it's not like her issues with identity can be explained only by her being a vessel or lost goddess or whatever - in fact, she has very good reasons to be the way she is: being raised by humans from very little, in a world where (as Solas says it) most people don't look beyond a pair of pointed ears. So, she never can really find her place among humans, while she also can't find her place among elves either. That's actually a fairly common psychological basis on which one can grow identity crisis.
And if the theory the Gods are connected and/or trapped to/in the Eluvian's is true, all these destroying them or using them might have awoken something.
So far we don't know anything about the eluvian that apparently holds the gods being destroyed or used. The post-credit scene suggests that it isn't. And according to Cole at least they (whoever THEY actually is) still "sleep, masked in a mirror".