Why does OS X now think I have two partitions on my external USB drive (plus random connection issue)?
Q1: any ideas why the drive not showing up … (sometimes it does, other times it didn't)?


If the file system is dirty at time of connection of the disk, then the operating system will run fsck_hfs until (hopefully) repairs seem to succeed. During this period the volume will be not mounted, and the OS presents no alert. 

(An alert appears only if, for example, repairs are unsuccessful.)

In your case, as CoreStorage is used to encrypt the logical volume that is used by Time Machine, there's also fsck_cs.

For your ~1 TB file system that includes backups written by Time Machine: if repairs are necessary, fsck_hfs may take an extraordinarily long time. 

With Console you can browse

/var/log/fsck_hfs.log