The old unwritten rule used to be if a program has a shrink button its OK to shrink it and do other things while its running, if does not have a shrink button you should let it run and not attempt to do anything else. The latest AVG version has a shrink button so do you think it is OK to shrink it and do other things while its running. I wasn't sure if that's OK with an anti-virus program

You should be able to do other things on the computer while running an antivirus scan. I wouldn't be running a demanding game though, as it would tend to lag.