Fitbit sync

Correct, it only adjusts your calories. If you are doing something that it doesn't track well (pretty much anything other than walking / running) you can log your exercise as normal in MFP and when you provide the duration and time of the exercise it will sync back to fitbit and remove the calories it has added in favor of the calories you told MFP for that activity.

Re: eating those calories; remember that your goal in MFP is already calculated including a deficit; eating back the calories that MFP or Fitbit gives you back doesn't change that deficit it maintains it. If you eat back your calories (and everything is dialed in correctly) you will still lose weight at the rate you set up in MFP since you are still at a deficit.

Also, you have to opt-in on the fitbit settings to receive a negative adjustment. Otherwise if you do nothing af all all day your fitbit won't change your calories for the worse it just won't add them. If you have negative calories turned on you'll likely be 100 to 200 in the hole first thing in the morning and you'll have to be active enough to get back up to 0 before it starts adding more. Some people don't like that but I prefer it.