There are three Underground stations at LHR: one at T4, one at T5 and another serving T1,2,3. From Arrivals at T2 simply head downstairs and follow the signs for the walk to the station. There are lifts down from Arrivals and travelators en route to help speed the journey. The walk from Arrivals to station should take about seven to 10 minutes.

Unless you have a Travelcard for zones 1-6, you'll need to purchase the excess fare for the journey from the airport to zone 2 before you leave LHR.

No, all the Terminals have direct access to the Underground. There is only one Underground (not a regular or Express) and I think you may be thinking of the Heathrow Express, a train service.

To repeat, all Terminals have access to the Underground and all Underground trains go to Piccadilly Circus.

There is a tube terminal at T2 no need to go anywhere else. Just get on the tube there, it goes direct to Piccadilly Circus.

There is no such thing as an "express underground" (in the sense of the tube), I presume you are thinking of the Heathrow Express, which goes to Paddington, but that's not on a tube line (and your pass isnt valid for it anyway)

Is your travel card good for Zone 6, as it needs to be?

Thank you all for helpful tips.