SQL Server : Restoring database mirroring once its turned off
ALTER DATABASE dbname SET PARTNER OFF will break mirroring. See this answer. You will have to reconfigure mirroring again. So option 2 is your only option at this moment.

The answer that I linked has an automated script that will help you.


  Would simply turning on database mirroring solve the issue? , Would the transaction logs automatically update?


No, since you issued SET PARTNER OFF, mirroring is broken. Now you have to initialize using a full backup and latest transaction log backup from the primary server to the mirror server.


  what's the best practice to resolve a split brain issue?


Next time, first turn off (remove) the witness and then do SET PARTNER FAILOVER as I have detailed in my answer.