Welcome
, there is plenty of great info here & you just need to have patience with your searches.
I'll give you my two cents on some of your questions.
The tow hook - that would be your choice, if you like on then leave it.
Blind spot mirrors - you will get different responses to this one. Some people say that if you adjust your mirrors correctly then you don't need the little blind spot mirrors. As for me I put those little stick on mirrors on every car I own. Gives me a little peace of mind about what is coming up on me.
Battery - Since this is a 2012 Z it would be hard to say just how long the battery has been in the car. It just might be getting old & needs replaced. Try giving it a good charge & see how it does.
As for the camera & the exhaust smell I can't help you there.