Does a flare up last for months? Do the sxs of a flareup sometimes stay permanently?
A flare can last for months, or it can be shorter in duration. Often the symptoms of a flare remit, sometimes completely, sometimes partially. But, yes, they can remain permanently. These are often referred to as residual symptoms.

Do some sxs dissipate and others stay when a flare lessens?
Yes; this can happen. Some symptoms may go away, while others remain.

How does the neuro know if you're RR or SP? How do you know if you go into SP from RR? Not that I want to find out, just curious.
NMSS says that, before the disease-modifying medications became available, approximately 50% of people with RRMS developed SPMS within 10 years. It likely takes longer than that to develop SPMS, if you're on a DMD, which is designed to delay the progress of the disease. If you have SPMS, your disease would progress more steadily than before, and, you may or may not continue to have relapses.

~ Faith