When you fail over to the mirror, once the primary server is back online SQL will automatically being feeding the transactions back. When you look at the databases in the UI it will say if it’s mirroring or synchronized. If it says that it is synchronized then there are no pending transactions to be sent.
You won’t be able to initiate the failback until all transactions have been replicated otherwise your databases will be out of sync. Think of mirroring like it’s log shipping as that’s basically what it is. The difference is that with Log Shipping you are backing up the logs on a schedule where with Mirroring you are moving the data in real time or near real time.
Yes you can change the safty mode from synchronous to asynchronous mode by using the ALTER DATABASE command.
ALTER DATABASE YourDatabase SET PARTNER SAFETY FULL
ALTER DATABASE YourDatabase SET PARTNER SAFETY OFF