what destination should I book? I don't see Leeds Tempest Road in the National Express site.
National Express has only one stop in Leeds, which is the Dyer Street Coach station. From there you need to take other transportation (bus or taxi)
Will we have enough space to keep the luggage in National Express?
The bus has plenty of storage. What exactly you can bring and how much this may cost is part of the terms and conditions of your specific ticket.
Is any national express coach available after 9 pm towards Leeds?
No. It looks like there are only two busses a day: 8am and 14:00
Is it wise that I'm planning to prebook to avoid any delay when I arrive?
Maybe. This only makes sense if you are confident, that you can make your connection even if your flight is delayed and lines at immigrations are long OR if the ticket is flexible.
Heathrow has multiple starting points. Which one is the best?
T2/T3 is you arrive in Terminal 2
You may be better off taking the tube to King's Cross and then the train to Leeds. There are way more frequent itineraries and it's about 2 hours faster. Granted, wrestling luggage on the tube and on the train is not going to be fun.
If you are arriving only at 9pm all of this is a non-starter. Last train to Leeds leaves King's Cross at 8:30pm. If you are coming in this late, you should probably budget a night somewhere. It's 200 miles from Heathrow to Leeds.
Updated: Actually there is a connection through York (leaving Heathrow at 10pm). However that gets you into Leeds station at 2:00am in the morning, which may not be that useful.