my question is do we also have to go through Passport and customs and immigration.
No. You may have to show your passport at regular security checks, but you won't legally enter the UK, thus no customs nor immigration.
When you get off your plane, look for a board that indicates terminals for various airlines. If you have to change terminals, then follow the signs for "Flight Connection" where you will ride a bus to the other terminal. If now, then follow the signs to pass through security into the departure lounge.
You won't see your bags until you arrive at your destination.
Wear comfy shoes. You'll do a lot of walking.