It will burn but not catch on fire unless something nearby causes a spark. A/C current, especially on coil resistors, will sometimes give off tiny sparks that are enough to light something if it is very hot.
it will catch on fire, lol. all you need for fire is heat, oxygen, and fuel. the heat is from the coil, oxygen is in the air, and the paper towel is the fuel. something doesn't require a spark to catch fire. who even told you that?
Electric stoves, IIRC, have the coils below a thick glass.
some might, but not any I've ever used