Just how many people know about them, and care? Alternatively, How big a deal is it to be caught with one?

Could you walk into a hotel with a mask and a Fake Sin, and when it gets pinged, say "I'm a rock star, I just use this fake one to dodge the crazies?" and not get the insta-call to Lone Star?

I imagine as many people know about Fake SINs in SR as know about fake IDs today. That is, damn near every one. In your scenario you could pull off what you want so long as you succeed at a Con check against the person behind the desk. It would help if you had a few pieces of back up evidence (hot brainless girl on your arm, a dazed drugged up look on your own face, etc)

I doubt rockstars will have fake SINs, or if they have it's still illegal. Corps (and governments) can provide extra SIN when necessary (for example for a spy or an undercover agent) but they won't be fake SINs.

I doubt there's insta-call when a SIN is detected as fake. The SIN repository is known to be full of mistakes and prone to errors, and rulewise, the low rating fake SIN detectors are likely to glitch often. So I think that if the SIN is detected as fake, the guy behind the counter will try it again, unless you really look like a criminal (an ork for example) or the SIN is already flagged as potentially fake or belonging to a criminal. If the SIN fails a few consecutive checks, he might call the LS... or he might just tell you "I'm sorry sir, but there seems to be a problem with your SIN."