1. Hydroboost has a hydraulic accumulator. Just like losing vacuum supply to a vacuum booster, the booster has enough vacuum to supply power for a couple of stops. The accumulator stores enough hydraulic pressure for a couple of stops. It's entirely possible for the accumulator to go defective, though.
2. My '97 K2500 7.4L has hydroboost and EVO. (At least, there's what looks like EVO parts by the PS pump.) I don't think it works, though--steering seems pretty light all the time.
3. PS test systems are readily available for purchase. I don't expect most parts stores to keep that in their loaner-tool program, however.
4. Since I don't have PS test equipment, when it's me I pull the pressure relief valve out of the back of the pump, and look for debris/clogs. If I don't see any obvious problems, I'd replace the entire pump/reservoir/pressure relief with a suitable Treasure Yard item.
5. Yeah, I suppose you could have a defect in the steering gear or in the hydroboost that's causing low pressure system-wide. I'd suspect the pressure-relief first, pump second, though.