It's not the pressure, it's the volume of fuel that the pump can push. Remember that these have a constant flow fuel system like a gas engine with EFI does.
Yes after running or a while. I can't say how long it will take though.
The best starters are generally considered to be a Power Master 9050. They are high priced though. A m a z o n has some cheap ones listed for under $150. They are probably Chinese made and might not last very long, but would do for at first. I had one that lasted for 6+ years. It was still working, but I was having battery issues and thought it was the starter. I put a Power Master on and it didn't fix the starting problem. It did, however, spin the engine faster than the cheap starter did. If you buy one from A m a z o n, you'll want one that has a solenoid that looks like it's as big as the starter body. Parts store starters are a crap shoot these days. They may last for several years, they may only last a few months. The only parts store starter I bought did last for about 10 years so I didn't get hurt that way.