Columba folder w/mountain 10sp cassette & Sram X7 derailleur
That shouldn't be happening - it sounds as though you have the wrong hanger on the bike. If you have replaced the hanger (or a previous owner has) they have probably used one that fits on the bike but isn't correct. You may be able to file it down to fit, but it's better to buy the right hanger.

For your second question, it's definitely possible to swap out a QR axle for a solid one. The threaded part of the axle is the same for both, so it's just a matter of getting a solid rear axle and swapping the bearing races and so on over.

If you get that done at a bike shop they will probably suggest replacing the cones and bearings, since those are fairly cheap parts and the labour cost of taking the wheel apart is most of the cost of that swap. Once they have it apart if there's any visible wear it's worth doing, and unless the bike is fairly new I'd suggesting doing it. It should add less than $20 to the total cost.