Time Machine does not seem to be backing up my external drives

Hello all! I've had some problems recently with Time Machine, and I really don't know if I'm just an idiot or if this just isn't working. I've really tried doing a lot of research online and I cannot figure this out!

Anyways, so my backups were running just fine. Then I bought a new external drive that was much bigger so I could hold more backups on this. I used SuperDuper and cloned the old drive to the new drive to keep what backups I had. Then, in Time Machine preferences, under "change disk" I selected the new drive as my Time Machine drive. I should mention that pretty much every time I restart my computer now, I have to do this, as Time Machine will see the drive, but it is a different icon than when I select it as my backup drive (it turns turquoise). I don't know if this is a problem in itself, as it seems the computer needs to "re-see" it every time. I should also mention that yes, I did format the new drive correctly as according to the specs online (Mac OS extended journaled, etc).

So I've been trying to run backups for a few weeks. First off, I have noticed that the backups will only go back so far. This is probably due to switching drives. I've been backing up since about 2013, but this drive only goes back to March 2015. Second, most of these are greyed out, both in the "ticked" timeline at the right, and in the finder windows in the "Star Wars" view (when you enter Time Machine). I've managed to see some of these by holding shift+command+C. However, that only brings up backups that apparently, are only on my internal Mac hard drive. I don't know if this is also part of the problem, but I read you should find your .com preference for Time Machine in the library, and then trash it, so it can start anew. I'm guessing maybe this is why I can only see up to March, as that is when I got the new drive.

The third issue is that when I turn on my external drives, I see them all the way back to March, apparently "backed up"? But I know for a fact some of these haven't been backed up that far back, because one has been in a closet for a while and I just brought it out a few days ago to test it. So I'm not sure why in the STar Wars view I'm seeing it all the way back to March. Second, when I unmount the drives, I don't see them at all in any backups. Aren't you supposed to be able to see your backups even if you unmount them? I had a drive that was probably about eight years old fail and needed to find its backup again a while ago in Time Machine because it wouldn't mount, and I found it and re-copied it (this was when I used my old drive before I did SuperDuper and the drive replacement). I'm not understanding why if I simply turn off or on the other external hard drives why I would see these in every backup, when they aren't even backed up.

Also, sometimes when I try to backup, it takes probably 2 minutes. I don't understand why it is so quick, especially if I have two external hard drives on and ready to back up as well as my internal Mac drive. I have checked in the "option" tab in the preferences window, and I do not have those drives excluded from the list of things to backup, so they should backup (and take a good long time to backup at that, I would imagine).

For the record, I'm running OS 10.5.8. Yes, I get it, I'm behind. However, I've never had any issues with my computer until now, hence my hesitation to upgrade. I would guess this isn't the issue since the backups were working before I got the new drive, but I have no idea. Any input would be extremely appreciated. I just want to be prepared in case a drive fails again, or something like that. Thank you to everyone!