To your first question: they probably won't notice the register being off by that much. I don't think it would hurt to let them know in case it comes up later, as you're still new and learning. Also, you wouldn't be over by $20, you'd be under by $10. Being over means you haven't given enough change back (total is $10, guest gives $20, you give back nothing. The register thinks there is $10 less than what is actually in the drawer, thus your drawer's actual total is $10 over the computer-counted total). Being under means you've given too much change (Guest pays $10.52 in exact change, claims they paid with a $20. Cashier believes them and gives a $10. The register thinks there's $10 more than what's actually in the drawer, thus your drawer's actual total is $10 less than the computer-counted total).
If any situation involving cash comes up you should immediately call over your supervisor (GSA/GSTL). They'll call AP or an ETL to review the video/register logs. If it's a scam they'll probably give up at this point. If it's not then they'll get the guest their correct change. Under NO circumstances (unless you absolutely know you made a mistake - meaning you were paying attention, counting out change, and YOU realized you made a mistake - not the guest pointing it out) should you open a drawer to give a guest more change than you originally thought they should get without supervisor approval.
If you don't work Cashier often you don't really need to worry about the speed scores (that's what R, Y, and G are). Nobody really notices the scores of the cashiers unless they drop really low consistently (like R for a week). It's also very un-important as far as metrics go. If a cashier that gets a lot of redcards is consistently red on speed scores they'll ignore the speed scores because redcards are far more important.
