If several known good batteries are used and you still have the same issue in stand-by mode + heating up of the device, then you may have a board level defect, such as a short (this would consume power and warm up the phone) or a defective chip.
Also, 3 hours to fully charge your iPhone is not normal. It should be way less than that. This also converges with a short since a short will consume part of the power coming through the charger, and delays the filling up of the battery.
Finally, something makes no sense: how come in stand-by mode you get 3-5 hours of autonomy, and while using it you get more (6-7 hours)? Are you sure?
Anyway, I would try to isolate the issue before concluding that it is a board level issue.
- Look at Settings>Battery>Battery Usage. What are the apps using up the most %? Last 24H and last 7 days?
-Also try and turning Airplane Mode on. Does it improve? If yes, leave Airplane Mode on, but turn Wi-Fi on. Any change?
Report your findings here if you'd like us to follow up.