I have an HBX Survivor that has become a bit crazy, sometimes gets stuck at full throttle. Have read that others had the same problem with that car. My question is whether it is possible to buy a remote control from another brand and make it work? Maybe change receivers too? I'm new to these RC cars and do not know how it works.

With any decent RC car, yes. You can change the transmitter and you need to change the receiver as well which comes with a transmitter. Just plug the connectors from the speed controler and steering servo over to the new receiver and recalibrate the speed controller. But....

Your car seems to have an all in one module which is very comon with such small and cheap cars. The receiver, speed controller and a part of the steering servo are in one housing that can not be pulled apart. Then you do need to change it all which will bring you close to a new car.

If it mechanically gets stuck at full throttle I would open the transmitter. Otherwise if you still have warranty I would go into that direction.

unfortunately has no guarantee left. the gas does not get stuck mechanically, it goes back as it should. When I turn off the remote control, the car stops. I guess the remote control is the problem?

High chance it is.

If it is something with the micro controller inside or the potential meter is a guess. The most simple thing you can try is to spray some contact spray into the throttle potential meter. On the other hand you probably can buy another transmitter for a few bucks (search on Aliexpress/Banggood).