Heathrow Transfer Advice

At the end of November I am booked to fly JFK-LHR UC on VS004 arriving at Terminal 3 at 07:10. I then have a flight from LHR to VIE on British Airways, departing at 10:55 from Terminal 4. I wonder if some of you old hands could give me the benefit of your experience and answer a few questions for me. First, should I be able to check my luggage through from JFK to VIE? I couldn't get a direct answer to this from either Virgin or BA. Next, assuming that I don't have to clear customs in London, will I have time to take advantage of the Revival Lounge before transferring to Terminal 4? Last - I am somewhat confused because some Heathrow information websites say that the T3 to T4 transfer is by bus and others say that it is via Heathrow Express, free of charge. Which is correct? It would be a great help to me if I could have a clearer picture of what to expect as I'm not as young as I used to be! Thank You!:)