I've been busy and not had time to check on my families for 2 days. When I checked, my three families weren't there. I don't know if they died, or, because I was installing my first mod, the mod might have interfered, but I'm still unsure. I'm wondering if I should back-up anything/start over?

Without knowing exactly what might have happened to the files, I can't say for sure why your families aren't there. However, you can go through this procedure in our Support FAQ to see if you are able to recover the files.

I think I figured out the problem: I thought the savegame files were empty files I accidentally created while installing the mod, so I moved them to the Recycle Bin. Is there any way to get them back, or are they gone for good?

If you have not emptied your recycle bin, you can open it and have it restore the appropriate files. If you have emptied the recycle bin, unfortunately, they are gone for good.

Is there any way to back-up the files without needing to have the savegame files?

The savegame files contain all of the information about your games-in-progress. When you run the game, it loads the information contained in those files to let you continue playing where you left off. Without them, the game program will start from the beginning.

So, LadyCFII, everytime I try to play the game it will start from the beginning?

Once you start the game and create a player name, a new savegame file will be created, and you can continue to play that game.