Carry over mode is an option you can choose if you lose a fight. It lets you keep any money you earned by killing things in that fight. However, if you use it, you won't be able to work towards getting a bunch of achievements. Not worth it unless you've already collected all the achievements imho.
I can agree with that, carryover mode doesn't really serve much of a purpose, it's worthwhile to just remove it so people don't miss the fact that they could just choose to go to the main screen and load the game from the last save. (Which allows you to get medals btw)
Probably could just set it up like people are used to seeing it: Just put on the main page, Sandbox/Normal/Hardcore modes where choosing one greys out the other two.
Getting the permanent +1 hp does not cancel out perfect game. Heh. You have to fix the castle after you get that message to bring yourself back to max health. Otherwise, you're starting the wave at 45/46.