If your snakes are only 3 months old then no, it is not eating because it is breeding season. Chances are you have a husbandry error that is stressing the snake out.

You should quarantine in another room in your house for at LEAST a month. Most people will recommend 3 months.

You could just feed one adult mouse, a rat pup and an adult mouse are about the same size.

No, you just need a new light.

Lamps are really not recommended for ball pythons. Ball pythons don't need any kind of spectrum lighting or overhead heating at all for that matter. You are better off ditching the heat lamps for under tank heaters.

Well, you don't need to use bulbs at all. If you are using one to keep your temps up, it should be on 24/7 night drops are not really recommended.