As you suggest yourself, an HIV rash
and fever cannot clear up in a day or two; acute HIV symptoms
last at least a week, generally 10 days or more. And when we also consider your sexual history, it is simply not a realistic possibility you have HIV. Even if your partner had classical symptoms of acute HIV, it would be pretty much impossible for HIV to be the actual cause.
So the direct answers to your questions are 1) no, 2) yes, 3) could be but this doesn't matter, and 4) yes.