Is it possible to use the external WiFi dongle RTL8812AU (for the better range) to connect to the hotel WiFi router - and to connect my devices to the internal (weaker) WiFi of the Brume-W ?
Yes you can. The firmware can handle two wifi radio.
it is possible the same thing but with beryl?
Very unlikely for the same thing to be possible with Beryl, because MT1300 comes with MTK proprietary wifi driver
If you want to use an external USB Wi-Fi adapter for longer range, it seems that Brume/Brume-W and Slate (GL-AR750S) are better choices than Beryl
I’m using the suggested Alfa 1200AC model, working ok so far?