Free travel at Heathrow :
Heathrow Express/Connect. No ticket barriers to the platforms, and tickets are not checked on the sections inside Heathrow. They are checked when the train moves on beyond.
Underground. Only free if you have an Oyster card (any sort), with some money on it, to get in and out of the ticket barriers. System is programmed so if you go in one Heathrow station and out another, a fare of 0.00 is charged.
Bus. Inbound to Heathrow, driver just stops taking fares/Oysters at the boundary. Outbound you need to tell the driver if you are only going within the free zone.