There is an AC paid waiting room at the Falaknuma end of PF1 at KCG. Used it in Dec and looked quite usable and clean. The bathrooms were good too.
Rs 20/30 ( dont remember) for first couple of hours. Had a seating capacity of 30 but there were hardly 4 or 5 of them when I used it on a weekday in the afternoon hours.
I'm not very sure about your intra-city travel questions but a MMTS is most recommended to catch your return train from KCG.
As...
more... for food, there is one good place on the PF itself, close to the waiting room (near the FOB) on PF1. They had good stuff there. I had my breakfast and dinner at the place. Plenty of options to choose from. Haven't had a better noodles and veg ball Manchurian especially inside a railway station.