1) i say push. if you push it costs you 400 and then the pot(combined) is 1200 total. You should have at least 11 outs (3 might be ties) and will win over 1 in 3 times. I think PFR has AA/KK and BB has JT or a set. you have 11 or 12 outs, and the odds to put it all in.

2)I think sometimes people over defend to a steal. He might not realize how strong you are and may have AK or possibly even AJ or AT(not likely). You have also put a lot of money in the pot already. you are too strong to fold.