i'm new to this as well McArnar, there is a "workaround" thread but its pretty dated and none of the workarounds seem to be applicable anymore. I have all of these same issues, clipping doesn't seem to cause any problems apart from aesthetic (spelling?) issues and we just have to deal with it. Invisible characters and crashing when you shoot at them happens to me as well, especially when i try to load a tacmap save (which i only do after a CTD, im not one of those reload after xenonaut dies types). and the combat hangs are a constant problem for me too. apparently removing civvies fixes the issue but i did that a couple of days ago and still had plenty of problems so i put them back in as the game is so much more immersive (lol at spell-check, maybe i spelt it wrong but it wants to change "immersive" with "immersible", is that some kind of submarine with an awesome suspenseful atmosphere?) with them in there. Somebody JUST posted a fix for invisible aliens but im waiting for him to reply with a little more detail on how to do the workaround as i don't want to destroy my game files.
ps. i had alot of issues with corrupted save games early on and one of the workarounds that seems to have worked pretty well so far is NOT to save the game when there are ANY aircraft OR terror missions OR crash sites on the map ie. only save when the only thing visible on the geoscape is your base.
Also tacmap saves almost always become instantly corrupted for me and if i can get them loaded without an instant CTD when i click loadgame, the map loads up and all characters are invisible and the game will CTD as soon as i kill one.