Jenny, its called a cloaca. Axolotls do not have testicles, which are commonly referred to as 'balls'. You need to learn this. When a male gets into breeding condition, yes, he will follow around a female. If she doesnt want to mate, then they wont. Are you prepared for 200 babies? If not, I suggest you separate them
Its an LED fixture, not a regular lightbulb. It wouldnt fit into 'any light fixture'. From what I gather, its a seperate fixture. Like a lamp. However, it seems like a waste of money to me. Axies dont normally 'forage' and they do so by scent, not sight.
If your male has lumps, it could be serious. they could be abscesses or gravel stuck in the intestinal tract. You should take him to a vet familiar with herps and get him checked out.
PS: They're pot-belly pigs, not popped belly