Answer to Question 1. -  No.  You are not required to return to the same
inspection station, however if you don't, you will have to pay the full
inspection fee again.  If you return to the original station with the
problem(s) corrected, they shouldn't charge you again because you've already
paid... some stations charge a dollar, I think, others don't.  I think it
depends on how well you know the station people, and how good of a customer
you are, or have been.  If you're basically a stranger who never uses their
other services, you may get charged a small reinspection fee.

Answer to Question 2 - Not to my knowledge.  Now, having said that, the
inspectors are accountable to the Va. State Police, who can audit anytime
they want.  Each station must account for each sticker issued, and at some
point, must report and/or turn in the little receipts for each sticker
issued... that's why they keep them under lock and key in a cabinet that
nobody besides the inspector can get to.  Do they eventually get to the DMV?
I don't know for sure, I don't think so.  Everything these days is
computerized, so maybe the info goes into a database somewhere that's
available to the DMV.

Free Advice -  Do NOT scrape off the sticker and drive the vehicle without a
sticker.  Unless your car is registered as an antique, it is worse to be
caught driving with no sticker, than it is to be cited for driving with a
dead sticker.  I don't know what your car was rejected for, but if I were
you, I'd fix the problem and return to the same station to get a good
sticker.  If you have a complaint about the inspection station itself, or if
you think they're trying to sell you services you don't need, call the Va.
State Police.  If the station did something wrong, they could loose their
inspection license if it is a serious offense.

Just my $0.02