I would think a simple time-delay relay such as this would work for AK's scenario 4.
It could be powered by the signal from the pressure switch and one of the NC contacts could control the pressure motor relay.
A NC push-button in series with the relay power will reset it.
It could be powered by the signal from the pressure switch and one of the NC contacts could control the pressure motor relay.
A NC push-button in series with the relay power will reset it.