do this. I've also been in your position.
1. If they ask for example how they could of made the experience more positive for you, theres nothing wrong with providing honest feedback and I imagine would be welcome.
3. Two weeks is the standard, but yes you will have to do whats best for you and your new opportunity. I wouldn't jeopardize your new opportunity, in case they ask if you can stay a little longer than expected.
4. Thank you email along with contact info. You never know what happens down the road.