I have recently decided to take online courses but I had a couple of questions going on, in my mind. I was thinking if I would be able to apply for student permit based on my admission in open university. I know that the university is actually UK based but maybe through one of their branches in Switzerland, I would be able to apply? I can't find any information regarding their branch in Switzerland (don't know if they even have an official branch here).

Any help is greatly appreciated.

No, they don't do "branches". Study groups, maybe even tutorials, and certainly exams, may be arranged here, but it's a UK institution only.

No idea how student visas work, but I think it very unlikely to be appropriate.

Nope. It is extremely unlikely that you'd be entitled to a Swiss study permit. It's a fully UK-based institution, not a Swiss university and while they might have some local exam center, study groups, maybe even "live" lectures, they have no branch in this country and have nothing to do with Switzerland or the Swiss education system.