You also have to compress it to very high pressures to be able to store a useful amount of it.
No, it's not. Electrolysis is extremely inefficient. There are some modern developments with advanced catalysts, but it's not something an average person can do.
Yes but in quantities I can use the drive my car?
If it's simple, why practically no one is doing it?
Last I heard, 99% of all H2 was produced out of methane. Perhaps it's a bit better now?