"1. Is there only one Panel Design on the Master?"
Yes. It is easy to overlook, but the reference to this is included in our "Things of Note and Tips" section in the TPControl - BYOD How Toguide.
"How can I use one BYOD Licence when I have one Master controlling two or even more Rooms?"
I consider this use-case to be similar to if I was using a MVP-5200i/MVP-9000i or other AMX panel i.e. you would design a single UI file that is reusable for each of the rooms you intend to use the device in. If there are specific differences between each room, simply add the related pages/popups to the single UI design, and when the device connects to the AMX system update the content via AMX API calls and even prompt the user for location/room if need be.
"2. How can I make sure everyone stops controlling the room when they end their meeting? Not disturbing the following meeting, for example, playing with the app."
This can be addressed by designing the AMX code in a way that specific access is granted to a device after entry of a passphrase or pin-code perhaps when the device connects to the control system, and furthermore building in a time-specific time for "control" of the rooms functions e.g. perhaps the AMX Device ID you assign the device only gets "control" for 1 hour or some custom amount of time. At the end of that time, buttons presses/interaction from the device could simply invoke the need for the user to again enter a (new) pass-phrase or request permission from a room booking administrator. In this manner, management via customized AMX code determines the device ID's that have "control" of any given room.
You can appreciate that you cannot stop people connecting to an AMX control system if they know the relevant connection settings, but you can hinder them from doing anything useful by managing how the device can interact with code that is crafted by the programmer. Passphrases/pin-codes etc could be something administered by a Room booking administrator/agent that is updated and accessible to the control system through various AMX programming techniques. Another idea could be to perhaps displayed in each room the specific passphrase/pin-code needed to control the room which refreshes periodically and requires re-entry when it updates/changes.