Clean up PartitionSettings

The PartitionSettings struct contains some data elements that are duplicates
of data elements in the TWPartition class that is contained within the
PartitionsSettings.Part element. We will eliminate this duplication to help
reduce the chances for programming bugs.

Specifically, this fixes problems where the current file system does not
match the backed up file system.

Change-Id: I02f236e72093362050556a2e53a09d1dbb9a269d