Q) When changing the dates it no longer synchronizes tasks

A) Where are you changing the dates? Dates can only be modified in task list. 

Parent task:

If you have a summary task only the sub-task will be able to edit dates. 

Google calendar integration:

Dates can not be changed in your sync google calendar. 

Past dates:

Check the starting date of your project properties. If the date is in the past from the start date of the project you will need to change the start date to match.