O.k. here's your answer

From your description, the hose that connects the reservoir (gray with red cap) to the power steering pump is being "sucked" closed. Right?

This hose is not under any pressure, fluid is gravity fed to the power steering pump. One of two things is wrong.

1) The inlet tube (the one sucked flat) is old and needs to be replaced

2) There is some sort of obstruction in the bottom of the reservoir.

Either way, this is what I would do:

Drain the fluid from the reservoir, all you should have to do is remove the inlet tube and fluid should come flowing out. Replace this hose with one from the factory, it's probably around 20-30 bucks which sounds expensive when it comes to a hose, but compared to a new pump and rack, that's nothing.

Next remove the power steering reservoir from the mount and flush it with some sort of solvent. I usually use paint thinner, seems to work pretty well. Plug up the ends and shake it around for a while. Rinse it out with water. Fill it with water and hold it in the same orientation as it is in the car. Water should gush out of the outlet tube. If it doesn't you should either look harder at getting the obstruction out or get a new reservoir.

Good luck, this should fix your problem.

BTW, Power steering is a self bleeding system, the only thing you have to do is essentially use it... turn the wheel lock to lock a couple of time and no more air as long as the entire system is in good shape. This is because the fluid is fed by gravity to the pump inlet, then compressed and routed to one side of the hydraulic ram (power steering rack) while the other side bleeds it fluid back into the PS reservoir. Pretty neat system really!