The reason your school had squat toilets may have been due to lingering Moorish influences in France. I saw a similar thing in Spain about 50 years ago in rural areas, both water flushed and simply a slot over a pit. I'm not so sure about being easier to clean tough.
On this topic, my middle school had automatic flushing toilets. The seats were black, open in front and back, and were nomally at about 45 degrees to the horizontal. When someone sat down, the toilet flushed briefly and when the person arose the toilet flush for a longer time. There was some kind of mechanical linkage between the seat hinge and the flush-o-meter handle.
You mom was correct about not staining, but IMO wrong about using suppositories to make you poo if you had constipation. Suppositories don't soften poo… they just make one push out the hard poo which is just as bad for getting hemmies.
The other things she gave you would certainly help.
A mineral (paraffin) oil, in the right dosage, certainly softens poo and makes the inside of the bowel slippery so when you squat, the poo almost cannot be held and slides right out. The trick is to give a big enough dose to work, but small enough dose so you don't leak stinky oil.
Prunes have a well deserved reputation for being laxative, largely due to their high Sobitol content. Yes, they have a good amount of fiber, but that's not what makes someone poo. Sobitol is a poorly digested sugar, because we don't have the proper enzymes, so undigested sugars pass through into the large bowel. There it's party time for the the colonic bacteria and they release gas and irritating compounds and the person soon starts farting and pooing.