Faggots the flesh of an animal and the body parts of an animal ground up into a ball, fags(fag sing) are cigarettes not faggots.
An ass is the mating of a horse and a donkey.
Just like other countries, each area of the UK has its own particular words, if I travel 150 miles ,there are words I have never used, just because those words you've mentioned are used in one area ,they are not necessarily used in another area, Americans appear to think everybody from the UK lives in East London.
It is the same in the USA - drive 100 miles in any one direction and you will hear words, phrases and pronunciations different from the place you just left.
Asses are the same as jackasses here - they are donkeys. Horses crossbred with donkeys produce either mules or hinnies, depending on which one is the mother.
We have three donkeys as pets. In the winter, they eat a big hole in the center of the haybales where the dried grass is sweeter. Guess what we call those holes? LOL. We have lots of ass jokes around here. "Dumb ass" is perfectly acceptable when dealing with the donkeys.
One time when I was a kid, we had a student minister preach at our church. He got all wound up preaching about Good Friday and Easter, and actually said the Jesus rode into Jerusalem on Palm Sunday on the 'ass of a colt.' There was a lot of suppressed snickering from the congregation.