How long should it have taken the computer to back-up? I finally unplugged it at 1:15 and it said I was supposed to eject the disk in FINDER before disconnecting and Finder would try and repair any damage that was done...ugh.

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That’s a common warning you will see when disconnecting a storage device like a hard drive or USB key from your mac. The proper way to disconnect a storage device is to drag the icon to the trash. You’ll notice that the trash can turns into an eject icon. You did not do any damage. As for how long time machine takes to back up, that will vary depending on the last time you backed up. Commonly, plugging that TM drive up every day or so will only take a few minutes to complete the backup but in your case, where you went more than a week I’m guessing, it can take longer. The first backup can take hours.

Nothing to worry about.