You can gain levels in the game both by gaining exp from fights, and gaining femininity through events and transformations. The idea is that you can get strong enough to progress without any femininity, but it will be more difficult to do so. If you only want to avoid physical transformations, I don't think that will be very difficult. Some events will transform your body, and at least one is unavoidable, but you can undo the transformation cheaply afterwards. Also, as you reach the dungeons, you'll gain items to tweak the difficulty, so you can use those to progress more quickly without needing to feminize yourself greatly if desired.
As for game overs, there are none. When you lose to an enemy, a scene will play, you'll gain some combination of femininity and depravity, and then you'll either return to town, or if you are in a dungeon and have linking charges (basically healing items), you'll automatically recover and continue.