Can I just write and submit a paper to a conference?
Yes, absolutely anyone can write and submit papers. It's difficult to do a good job on your first attempt if you don't have any guidance from a mentor, but it's not impossible.
I'm a Master's student, and I'd like to write a thesis, but my grade's don't qualify me (you need at least a 3.75/4.0 GPA). Can I just go ahead and write on?
Nobody can stop you from writing something, but it won't be a thesis. You'll lack supervision from an advisor, which will make it much harder to do a good job, and even if you manage to do a good job the department will not accept it as a thesis. (Bureaucracies don't work that way, plus working with an advisor is considered a crucial part of the process.)