"I am really interested in learning some basic climbing skills. I want to know how to rappel and how to set a rope to protect myself while doing risky scrambling."
Rappel: the dulferstitz works. No harness needed. The Munter hitch on a big carabiner works without a belay device. Prussiks, Garda hitch, and other techniques are good low-tech ways of ratcheting up the rope.
Risky scrambling: buy nice approach shoes with sticky rubber. Rope-soloing isn't that complicated, but the problem is, I think you need to master 'actual rock climbing' before you can do it safely. So it seems like if you're using the rope to protect yourself during risky scrambling, you've already graduated beyond 'actual rock climbing.' But check it out and see what you think. Lots of good info on rope solo and solo aid on the web.
"I think that having learning some climbing skills could really help me on some of my hikes. I'm not interested in doing actual rock climbing. I just want to be able to deal with waterfalls, short drop offs, and short climbs."
So, just to reiterate, I think the best measure is to just wear approach shoes and solo it. Or bring some thin rock climbing slippers. 30m 8mm rando rope and no harness can get you back down.
"Where should I start? Where is the best place to learn these skills? I don't want to spend a lot of money and I don't want to waste my time learning skills I'm not going to use. Any suggestions?"
An old copy of Freedom of the Hills. Rappel out of a tree. Have fun and good luck!