Is there somewhere I go to learn basic at-home car repair/maintenance?

No one here even knows where you live so how would they know?

Tyre changing needs specialist equipment that if bought would cost enough to enable you to use that money to pay someone to do it as many times as most people would need in a lifetime of car ownership

Brakes - a massive safety problem as not all cars have the same systems and sometimes special equipment is needed for those too.

Spark plugs - removing and replacing the plugs is relatively easy with the correct tools but as car under hood layouts vary the things that may not be straight forward and will differ greatly will be what else has to be removed. In an extreme example that I happen to know about the engine of a car has to be removed to change the plugs as that is the only way to get at them.

I can see what you are after but having the correct tools to do some jobs, a space out of the weather and a repair and maintenance manual for a car is the best you will do. Even then you can forget some jobs, like changing tyres for example.

your area vocational technical school may offer community based education classes.