[dnanian]

You can add the backup drive into the Spotlight Preference Pane's "Privacy" tab to stop Spotlight from indexing it.

Glad to hear you couldn't actually eject the backup: that wouldn't make any sense at all. The internal not being ejectable might be because something is referencing it by volume name. If you name the backup drive the same as the original, it'll stop that from happening.

Again, don't check the startup drive by desktop position. That's just not legitimate: use the Startup Disk preference pane.