Transit area at Beijing airport terminal 3

There are restaurants and rest rooms but seemingly no hotel.

You will be able to access all the facilities located airside. You will not be able to access the facilities outside the area that we usually call airside or a sterile transit area located landside. In any case you will have enough choice airside and if I am not wrong, there is also one simple hotel airside, but do not take me for a word on that. In any case, this is your decision and you have to be aware that airside area in Beijing becomes quite boring after the last flights have departed. Most of the facilities close and you will have just the benches or that hotel at your disposal until the early morning hours. If you ask me for a recommendation, I would definitely apply for a temporary entry permit for free upon landing and have a decent night rest close to the hotel or even in the city as well as some decent food choice. In any case, it will be your sovereign decision.