I plan to arrive by road at Heathrow Terminal 4, but need to check in at Terminal 2 for my flight. Can I use the free shuttle service before checking in? Car parking is substantially cheaper for T4 but I would need to get to Terminal 2 before going airside. Of course, I appreciate that extra time is needed.
Yes, you can use the train or the tube to travel between terminals, both are free within the Heathrow perimeter. You'll still need an Oyster card or contactless payment card to use the Tube, but you won't be charged for the journey.
There's also a bus service, also free, take either bus 482 or 490 from bus stop 7. This may be more convenient for you depending on where exactly you park. All London buses (the red ones) are free within the Heathrow perimeter.
You do not need to be checked in or even travelling on a flight that day. These are free services for anyone travelling within the airport perimeter.