Is it normal to be gay but have really close female friends? Like close best friend level, but not romatically-interested level? Or am I biromantic (I'm not sexually attracted to females at all)?
Friendship doesn't equal romantic relationship at all. It is totally normal that you have close female friends - just the same way it is normal that you have close male friends or non binary friends. Your sexuality/gender does not define the kind of friendship you can achieve with a determinate gender. And of course, if you are a male and homosexual, it is totally normal that you don't feel romantic attraction towards your female friends!
Yes, that's so normal that it is in fact a well known stereotype! Straight women and gay men often have very close relationships. My friendship with some of my female friends (even girls I dated in the before-days) has grown pretty strong since I came out to them. I think it has something to do with the mutual trust that you can be very close, but the women feel that the men will never be interested in more. The way my friends tell it, that seems to be a really liberating experience to be able to cuddle with a guy without him wanting to have sex. Go with it, and if you do develop sexual (or romantic) feelings for a woman, work it out with her. Don't fret yourself now.