Is there parking at the temple building ?

No, but there are some Private Parking nearby and they make discount for temple goers

If you go on a Saturday, you can get a parking sticker for the parking garage on 66th street around the corner from the Temple. The cost for 3 hrs is $10. During the week, some garages near the Temple give you a discount if you arrive before 9 am. The best bet and the parking garage I use all the time since the Temple opened is over on West End and 62nd street. It is a bit of a walk (8-10 mind depending on your gait and the traffic lights) but the cost now is $15 for 8 hrs or less.

No. There are parking garages nearby that cost money, but the temple does not operate its own garage.