As far as breeding H. cinerea goes, I can speak with some qualification that these guys (at least) amplex rather readily: I have had one on my arm next to a tank without the screen lid, only to have a male jump from the tank and crawl up my arm to engage in amplexus!

North American Hylids are by far the most straight- forward of the family to keep in the average house at average ambient temperatures/humidity; The difficulty lies in raising the metamorphs to something that can accept pinhead crickets (try flightless fruit flies here)

Now, speaking in terms of disease transmission, it is very unlikely that your Thamnophis (marcianus?) is even "clean" of parasites to begin with, regardless of being the captive born snake that it is! Between feeding it lab mice, fish, walking outdoors and handling the snake in the same clothes and/or not washing your hands, your snake is harboring parasites.
The key to mitigating the damage that these parasites cause is to keep the snake in a “stress-free” environment with adequate food and heat so that it can maintain its immune system and keep these parasite populations under control.