I have a 2006 Volvo XC90 with a v6. It's actually a work vehicle so I don't personally own it and don't know too much about it.
For a while it had a power steering leak, and as long as we topped off the fluid (my boss never used volvo fluid, just general power steering fluid) we never had any issues with it.. other than the leak. We used a green dye that glows when you shine a black light onto it to find the leak and it turns out it was an O ring on one of the fittings going to it. So we fixed it and don't have any more leaks. But now the power steering sometimes completely cuts out when driving at low speeds. When you first start it and drive around it drives fine and normal, but after about 10 minutes of driving it will randomly get really hard to turn at low speeds.
When we added the fluid we burped the system by filling it up, leaving the fill cap off, and turning the wheel back and forth for about 10 minutes or so.

Is it possible there's still air in the system? We put probably 500 miles on since we last had to put fluid in it.
Does the wrong fluid have that much of an effect on it?
Do you think the green dye is effecting it?

 

Not sure how much the wrong fluid can affect things but it could mess with the seals in the system. I researched the same thing hoping to save on fluid and people seemed pretty adamant that the fluid type mattered so I went with the CHF 202 fluid.

Could be the pump going bad or the rack going bad. Keep your fingers crossed for the pump. Easier and cheaper to replace.

Accessory belt slippage could effect the pump by not allowing it to actually work. But I feel like that would make noise. But maybe the belt tensioner?