1. What is your Lavellan's name?
Cari. Short and sweet!
2. What is your Lavellan's class?
Mage, Knight Enchanter. A little OP but I like the idea of it. Like being an arcane warrior again!
3. Which god's vallaslin does your Lavellan use?
June. No special reason, I just liked the designs. I do picture her as good with crafting and deft with her hands, though.
4. How old is your Lavellan?
30 at the start of DAI.
5. Did you intend to romance Solas when you started the game?
Ohhhhh yes. I've been in this thread and on the Solas train for months. MONTHS. I remember back when we were all pessimistic and convinced that he wouldn't be a romance option!
6. What is your Lavellan's relationship with her clan?
A good one. They're her family and she's a type that thrives when she's surrounded by people she cares about. She was very lonely at first without them. She was also the Keeper's First so she had to be pretty involved. After the events of DAI it's unlikely that she'd ever return to them for good, though. Or that they'd even accept her back considering certain choices.
7. What are your Lavellan's religious views?
She believed in the elven gods at first. Now if you asked her, she'd tell you she just doesn't know what to believe anymore. She puts her focus on people and the here and now instead of gods by the end of DAI.
8. Did your Lavellan drink from the Well?
No. Too much risk for a benefit that might not be there. She let Morrigan take the plunge.
9. Did your Lavellan have Solas remove the vallaslin and why/why not?
Yes. I've gone into this before on this thread so I'll just quote it here with a couple things added.
My Lavellan removes them but I play her as becoming detached from Dalish culture anyways. She wants to start fresh after everything that she learned and that happened during Inquisition. She doesn't feel like she can truly go back to her clan as a Dalish elf after everything, even before the whole vallaslin thing. She sees the elves as a whole differently now and feels they should be united more than ever. I already said a while ago that I see vallaslin as a symbol of the Dalish clinging to a past that wasn't as great as they believed and that they don't truly understand. It's time to move forward. Cari wants to look to the future and work with what the world is now because it has potential.
If Solas knew the real reason she gave up the vallaslin, he'd probably disapprove! 
10. What response did you choose after Solas broke up with you?
The one where she pleads with him not to leave. It suited her character best and it has my favorite Solas reaction.
11. How is your Lavellan taking Solas being gone and how are you taking it?
She's upset but mostly she's worried about what Solas is up to. Because of the way he was talking when he broke up with her, what he says before he disappears and what he says through Cole, she fears what path he is forcing himself on because he believes he must. That concerns her more than the romance's end. She's too busy with the Inquisition and trying to put proverbial bandaids over the wounds still left all around Thedas to pine too much for lost love. She just tries not to think too hard about it and gather any little scraps of evidence as to his whereabouts that she can between her duties.
I'm taking it fine, myself! I just can't wait to see where they're going with this haha!
12. What would you give for a Wolf Hunt DLC?
My money. TAKE IT, BIOWARE.