Nothing of what you reported was ever reported by anybody else, and since these are the most supported and tested planes in GSX, and used by most people, it's strange nobody noticed it before. Yes, there will be a very small bump at the end of the pushback, but surely no crash.
The "hot brakes" problem, instead, has been discussed several times, and it's supposed to have been fixed by Fenix in the current version. However, some users reported that it still happens if you use FS Realistic "Ambient Wind" function, so you need to turn it off.