1) Is there a way to delete games from the hard drive but keep the save files? There are a number of games that I could delete if necessary, but I definitely don't want to lose any save data.
Most games have separate save files from the game files. If you go into the Data Management and there's three files (saves, game data, updates) then you can delete the game file and keep the rest.
I think the only major game with combined save/game files is Monster Hunter 3 Ultimate, but I'm probably wrong.