Q: If my cluster becomes partitioned and an existing node already owns the cluster core resources, will that node and therefore its partition keep the file share witness and therefore quorum?
A: Microsoft has a great article that goes into detail about file share witness arbitration; see Tim McMichael's blog post "File Share Witness (FSW) placement and the cluster group." Although this article is from 2009 and focuses on Windows Server 2008, the arbitration logic hasn't changed, even in Windows Server 2012 R2, and the content still applies.
This means the node that currently owns the cluster core resources will have the first attempt to lock the file share witness and therefore ensure its partition makes quorum and keeps running. Other nodes in the cluster will sleep for 6 seconds during the arbitration, and only after those 6 seconds can they attempt to lock the file share witness, which would secure its vote-enabling the partition to make quorum.