Yotel in Heathrow Terminal 4 from Terminal 3 and travelling on from terminal 2!

We will be flying in longhaul to Heathrow terminal 3 and were thinking of staying for a few hours in the Yotel in Terminal 4. We then fly out 6 hours later on an internal UK flight from Terminal 2. (Will have to visit Terminal 5 sometime in the future just to make up the set!)

Questions are:
How long and how easy is it to get from terminal 3 to terminal 4.

How long and how to get from terminal 4 to terminal 2 for the onward UK journey.

I know we will have to pass through customs but can we do this if our luggage has been checked on through to our final UK destination?

Would it still be a 2 hour check in time for the internal flight from Heathrow to other UK destination?

I've tried googling this but an just getting more confused!

Thanks for any help.