1. Auto-assign is fine, though it won't takes skills into account so you can always fine tune that to balance out troublemakers/diplomats, make sure Research skills are in Research, etc. Rarely if a guy is A in, say, Intel and Research and has +Shotgun Research, he may get put in Intel. He could even be C in Intel, B in Research (with an important Skill too) but if Research is full of A Research, he could get put in Intel since it's the next best place for him. So overall it's fine and it won't really damage you, but you can likely usually find small ways to manually improve.
2. Sort of touched on that... you need to manually balance out Troublemakers and Diplomats. It's not that big of a deal but if you find people with Skills getting sick, you may want to kick out some Troublemakers or at least see if every platform has some Diplomats.
3. Just means they're new... it disappears quickly after a bit of time.