Yes, the Dates, Assigned to, Task Title, as well as the Progress, Priority, Planner Buckets, Label and Comments have a bi-directional sync to/from Project and Planner.
Yes, the dependencies (both predecessors and successors) that are set in Project and go to Planner will remain in Project when the data syncs back from Planner to Project. When possible the task will remain automatically scheduled. However there are some conditions, such as setting a start/finish date [...]
No, at this time checklist items are not synced.
The task will sync but the assignment will be blank - there will not be a resource assigned.
The tool will wait for the project to be checked in and apply the updates.