So, the SINer quality means that a character has a real SIN.
In the second Crash, fake SINs could turn real.

Does that mean that such a character now has the SINer quality multiple times?

Put a little more emphasis on "could turn real". I'd wager that getting multiple SINs through the amnesty program using the same biometrics would be pretty tricky. More likely you'd end up with one real SIN, and a bunch of high-rating fake SINs that, although legitimately processed, might trip as duplicate entries. It's certainly a good reason for someone old enough to have dealt with Crash 2.0 to have a bunch of fake SINs.

No, not the SIN amnesty program. Just turned real - see System Failure. Thus, they all are real.

I think that, even if you had multiple real SINs, which I think that one person can have, anyway, if he has dual citizenship, say, it only counts for one SINner quality. You aren't really more on the grid if you have two real SINs. If anything, it could serve to confuse people trying to keep tabs on you, and negative qualities aren't supposed to provide a benefit.