Transit visa in Beijing International

I am arriving in Beijing T2 from Astana at 01:55, and due to leave from T3 on Cathay at 07:30. Do I need qualify for a transit permit even though I will need to change terminal, and will there still be an area I can rest?

I am also the holder of a UK diplomatic passport (I am currently working in Kazakhstan) - which I understand means I do not need an entry permit for China. I would like to spend a few days in Beijing on my return and need to be sure that I will be able to travel in & out on my diplomatic passport without needing a transit type. Can you confirm this is the case please.