No power steering, engine cut out but has restarted engine hot fan on, no warm air so take this as a belt problem?

Power steering is run from an accessory fan belt off the main engine pulley. Power steering has nothing to do with brakes. The belt may be slipping. Make sure that belt is tight. You should be able to push on stationary belt and get 1/4 inch to 1/2 inch deflection. Check the power steering level with engine running while it is warm.

By fan belt do you mean the serpentine belt that spins all your accessories? If so check the tension on the belt. The belt tensioner controls this. If the tension is good, then one of your accessories is likely not spinning like it should causing the belt to slow down when the ac is on, causing the power steering pump to not spin like it should. I would take the belt off, spin each component separately and see if anything is stiff.

Everything stops because the engine dies. I would see about having your idle adjusted or look for vacuum leaks.

I don't know model year? Is the radiator fan electric or belt driven? If electric look for electrical connector. Your water pump has to be driven by something. If fan is belt driven, some makes and models, that same belt drives the water pump.

It sounds as if you have a volume of air in your power steering system. This is causing the bubbling and also some of the noise you might be generating when you turn the wheels hard right or hard left. This air might have been introduced if your old belt was slipping so much that the pump was essentially not operating and fluid wasn't regularly circulating throughout the system. Another, more expensive possibility is that your old belt was slipping because the power steering pump itself was starting to fail, and the new, grippier belt is turning the damaged pump and showing you its lack of functionality.
The first and easiest thing to do would be to bleed the system. Open the hood and take the cover of the power steering fluid reservoir. With the engine off but the steering wheel unlocked, slowly turn the steering wheel all the way to one side and then to the other. Repeat this several times while watching the power steering reservoir. Is the fluid bubbling? If so, good, you're purging air out of your system. In general, this is easier with the front wheels off the ground, but that is not absolutely necessary (if you have strong arms).
Once you have purged the system, put the cap back on the power steering reservoir, topping it off if the fluid level has dropped to the fill mark. Now, restart your car and observe the power steering pump. Does it seem to be operating quietly and smoothly? If you touch the pump 1-2 minutes after the engine has been running, is it hot to the touch? It will probably be warm, but _hot_ is an indication that something is overheating inside the pump. Is the power steering fluid very dark colored or does it smell burned? This is also a sign that the fluid should be changed ASAP and that some internal damage may have occurred. Burned fluid isn't necessarily an indication that your power steering pump is bad. However, if after changing your PS fluid the new fluid quickly becomes dark and starts smelling burned, then it's probably time to start saving money for a new or rebuilt power steering pump.

remove the alternator, power steering and fan belts as they will no effect you car when engine is just running, the water pump runs of the timing belt, if it still squeals it you water pump.

SOUND LIKE ENGINE GETTING TOO HOT.THAT WILL CAUSE LOST OF POWER.CHECK COOLING CLUTCH FAN IF IT HAS RESISTANCE WHEN ENGINE HOT FAN CLUTCH IS GOOD.IF FAN CLUTCH FREE WHEELS WITH NO RESISTANCE WHEN ENGINE HOT.FAN CLUTCH IS BAD.THAT WILL CAUSE ENGINE TO RUN HOT WHILE DRIVING.

You could have four belt's.
Fan / Power steering
Fan /Alternator
Fan/ A/C
Air Pump

check to see if the serpantine belt is still there. It sounds like like it broke. this belt runs all of the accesories on the vehicle including the water pump. So if this happened it probably starting running hot too

There are two (2) belts total. The power steering belt also goes around the fan/alternator. Double pulley on the alternator/fan, single pulley on power steering pump. The power steering pump mounts above the alternator on the left side of the engine.