Hi,
I think that binding is generally not considered to be a good idea for developing breasts. My partner bought a corset and was considering buying an overbust one but we did some research that suggested (not conclusively) that it could interfer with breast development and growth. It may also depending on how tight the bind is. Your partner is doing this because she is worried about other people having a negative reaction who may or may not know she is "out", tell her not to worry and to tell people she has gynecomasticia (fairly normal male breast growth that a lot of men can get).
Really her family is her family, not yours, but yes I understand the whole "protection thing". She can always take it off and repaint her nails another day or just let her family deal. Not going might be considered a bit of an insult, but again that is her decision that she needs to make.
And thirdly, yes, you can still get pregnant in the intial stages of your partner taking estrogen. If you want to have kids, sperm bank ASAP. Sperm quality will diminish quickly with estrogen. Keep using protection, having a kid thrown into the mix of transitioning is not easy (I know of a few with very young children and it is TOUGH). It takes 6 months to year, if not longer for some, for the transitioner to become infertile.
