Can F-1 visa holders (students) currently on OPT create an LLC or form a partnership?

Yes, this would satisfy the requirement for OPT and would not violate your F1 status. However, I would suggest planning carefully when setting up such a business, particularly if you would like to explore options for when the OPT has expired. There may also be e-verify requirements if you are STEM -extension eligible for example. I would suggest talking with an immigration attorney before setting up any LLC or other corporate entity.

It is very hard to say definitively that you can do this, but you should talk to your school advisor to see if they have any problem with it. If they don't, you should be fine. Whether the business is a corporation or partnership should make no difference.

Yes, but what happens to the business when the OPT expires.