On eyes- Lots of people with green and blue eyes have them change based on what they wear, lighting, hormones (as mentioned), and other things.
On Dora, Faye, pizza, and beer/Zebediah's list- I kind of hope Claire doesn't out herself to Dora/Faye, for two reasons. If she does when they're drinking and pizzaing, she might get not taken seriously, shock them too much (making them just like "whoa, holy" instead of "oh! okay."), or something else. The other reason is that I fin it nice for her to just be a girl, not a transwoman, and keeping the other characters thinking of her that way would be best. Of course Marten and Clinton see her as female, but I imagine that with more people knowing will come at least someone who sees her just as trans. Could be one of Dora or Faye (unintentionally, of course), or someone else who either gets told by Claire or someone who slips up.
(also, why isn't Penny in? Pizza is being ordered, this is her chance!)
I'm surprised that there's less speculation of why she's looking for Marten. I'm also curious if she's going to hang out or be discouraged by his lack of existing (probably not, since she stayed for the "argument")