2- Fresh food 2x a day, start with a handful or two. If he eats it all next time add more.
3-They bob for lots of reason, it sounds like your guy is asserting his manliness. Try to not let him see his reflection, it stresses them out when they see that "other" big bad iguana. Again , he may or may not stop doing this. His cage IS HIS territory, and hes letting you know that.
4- Outdoors. Buy or build a suncage. This can be as simple as finding a indoor dog kennel on craigslist or a yardsale or building something fancy out of wire.
Every year people show up here saying their lizard ran away. Its just not worth the risk. I personally would get him used to being outside by starting out with just a few minutes a day and building up to longer periods but seriously, consider confining him for his own safety and your peace of mind.Another thing I want to add. Iguanas LOVE windows, try to set his cage up close to one, if you havnt already.
5- He may train himself to go back into his cage each night. Otherwise, you just kinda gotta do it, just go for it. The only way to get them used to handling is by handling. Some will settle, some wont. Is what it is :/
6- I think the grunting is unrelated to temperature change.I wouldnt worry to much about that. Its just another way to communicate-Unless there is an illness and your vet ruled that out. If hes been basking and is nice and warm and you bring him out to a room set at 70-72- the body is going to just cool down naturally. He may pic a favorite place to chill out, you might want to set up a warm zone there.