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[croc_hunter_penny]

If you aren't planning on breeding, it's probably not best to keep the male and female together, especially considering it is usually frowned upon to keep any snakes together anyway.

As far as the tree branch is concerned, as long as you treat it properly it should be fine. You can treat it by soaking in water for a few days, to kill bugs etc. Some people use a weak bleach/water solution. Also hit it with a spray of Top Of Descent if you're still concerned. It's good to have a can of Top of Decent around in case your snakes get mites. It can be sprayed in the enclosure with the snake inside, just remove the water bowl.

In general the diamond pythons like cooler temperatures than other pythons, so having a styrofoam box for one of their hides is a good idea, as well as a low-wattage heat source to not overheat them. I have read that overheating can lead to stress and early death in diamonds, but I have not had the personal experience. They can have a good basking spot, as long as they have a cool area to retreat to. As far as I know, hibernating is not necessary if you aren't planning on breeding.