If we take a chair, will we be allowed to take it into the cabin? Or are you normally obliged to check it in?
If it is a conventional wheelchair you won't be permitted to take it in the cabin as it will be too large, however you can use it to get to the gate, where it will be stowed in the hold for the journey, and should be brought to the aircraft door for you to disembark. There are fold up wheelchairs that will go in the overhead locker, they fold down to a size like those camping style chairs, my mum had one when she broke her leg, I think she got it from one of the newspaper sales outfits.
As others have said, in the EU assistance is provided free of charge by the airport, outside of the EU other rules would apply, but plenty of people regularly travel to Pakistan that require assistance, so I shouldn't imagine it would be an issue at all.
With regard to who to travel with, ME carriers are about the most popular nowadays to that region, PIA would mean getting to MAN or LHR but at least then you are direct, Turkish have become a very big airline recently and seem to have won a lot of fans, all I can say is that I wouldn't choose them, their recent safety record has been poor to say the least. If it were me I would use a ME carrier.