You want to run a stable debian kernel, not “bleeding edge” stuff from the backports repo. It’s likely that your NVIDIA drivers are not compatible with the more modern kernel, either for real reasons (they’re old) or because that’s how they were packaged.
No idea, I don’t arch.
Theoretically you can install a desktop amd64 system using the binhost without compiling anything (or if compilation is required there won’t be much), I haven’t tried though I have seen other users do it successfully.