It seems like you have a couple of issues related to your computers and their sleep settings. Let's address each of your concerns:
Issue 1: Thymes Background and Hard Drive Sleep
The thymes background auto-changes every 30 minutes, while you have set the monitor and hard drives to sleep after 45 minutes. You're wondering if the thymes changing will prevent the hard drives from going to sleep. The background changing every 30 minutes should not prevent the hard drives from going to sleep. The sleep settings typically refer to inactivity across the entire system, not just a specific component like the monitor. As long as there is no other activity keeping the system awake, the hard drives should still be able to go to sleep after...