The very first thing you need to do is to become accustomed to looking at how things operate and interact on a bike. You are focusing on the derailleur springs, but that is only a part of what moves a derailleur. The cable either pulls a derailleur or brake in one direction or allows the spring to move it in the other. If the cable is rusted, kinked, or dry where it passes through the housing both actions will be more difficult (or impossible in the case of bad rust). When something is comprised of several parts you need to isolate each one to determine the problem, rather than guess.

I agree that you should not spend much money, and not a whole lot of effort, on many department store level bikes, especially Roadmaster, Huffy and Murray. Some other brands sometimes sold in dept. stores are not so bad - Schwinn being one example. You seem to have reasons for working on the ones you already have, and of course that's fine. But there are a good number of better bikes available at garage sales (preferable because you can see them and prices are usually better) and Craigslist or similar (not as good because "flippers" often improperly fix the bike and sometimes hide problems but charge you for a "fixed up" bike). I personally think your dad's 3 speed is the one you should tackle once any immediate transportation needs of your own are addressed.