I was looking at getting the Single Park tickets ( to save some $$$ ) and was thinking of going to NBA City for lunch or dinner. On the same day....is there "in and out" privileges to leave IoA to go over to NBA City and then to re-enter the IoA with the Single Park Tickets?

IOA is a very manageable park, you should have plenty of time to eat lunch at NBA. Also, it is very close to the park entrance...walking distances at Universal are very small, nothing like at WDW.