Should I Learn to Ollie While Moving?

Ollieing while moving is actually easier if you know how to ride. Doing tricks while moving makes it easier to roll when you fall and your brain and muscles can adapt to the movement of your board. Sure, it will take some time to ride a skateboard properly, but in the end, you'll progress much faster.

Should I learn ollie stationary or moving?

Moving. You'll have to learn moving eventually anyhow and learning stationary can teach bad habits.

Should you learn skateboard tricks while moving?

There's no right or wrong way, but you will have to learn them moving eventually. Just riding around in general should help too.