The answer on leaning is the cylinders get hotter and can get hot enough to damage them if you let them. But you're also going a lot faster than a car and hopefully cooling them more efficiently. So you either monitor the cylinder head temperatures or you don't push operations that might get them into elevated ranges - super lean operations, extended slow flight etc.
A question I didn't see answered is about what's under the hood. As I'm sure you remember, there are regulations related to who can work on an airplane and limits on what they can do. A pilot can do very little and that's good because you don't want a bunch of other goofballs tinkering with the engine that you're flying behind. If you own the aircraft you can do a little more, change the oil, service the spark plugs, etc. 14 CFR Part 43, Appendix C, section (c)(30) tells you what an owner can do, which is basically the items listed in section (c). Some very capable owners develop a good relationship with their A&P mechanic and do work under supervision with the mechanic inspecting and certifying the work performed. Other than that, you need to be a certified mechanic to work on airplanes.
Speaking off spark plugs and fouling, they shouldn't. Fouling indicates running too rich. They should be a nice dusty grey color.