I haven't seen any evidence that there were two shooters. From what I've read, the killings in the dorm were the first. Maybe he did plan to go on a full rampage, and just started with his ex-girlfriend and the Resident Assistant who came to help her in her argument with the killer. But the police responding to the first shooting didn't have any inkling that the killer had planned anything else, so they were not prepared for what he did next.
You are correct, first gun purchased 13 march, the second last week.