[mikeash]

Regarding your last part, some rockets have balloon tanks, which means that the tank requires pressurization to keep its shape.

The Falcon 9 has a sort of partial balloon tank. It's strong enough for ground handling without pressurization, but it requires pressurization to handle flight loads.

Note however that it's pressure, not fuel, that provides the extra strength. These tanks are still pressurized even when almost empty.