in transit 14 hours in Beijing? visa for Costa Rican?

My wife and I have a trip to Singapore next week and currently have tickets from Singapore to Beijing on Singapore Airlines:

SQ806
Singapore Airlines
(Boeing 777-300)
Departs
Singapore (SIN)
16:55 (26 Jan)

Arrives
Beijing (PEK)
23:00 (26 Jan)
Total travel time
6hrs 5mins

Then on to Germany:
Mon., Jan. 27, 2014 | Beijing, People's Republic of China (PEK - Capital) to Frankfurt, Germany (FRA)
Depart:
11:30 a.m.
Mon., Jan. 27, 2014
Beijing, People's Republic of China (PEK - Capital)
Arrive:
3:00 p.m.
Mon., Jan. 27, 2014
Frankfurt, Germany (FRA)
Travel Time:
10 hr 30 mn
Flight: LH721
Operated by Lufthansa.
Aircraft: Boeing 747-8 Intercontinental

We will be in Beijing 12 hours and 30 minutes. My question is if my wife (Costa Rica passport) needs a visa to spend the night of Jan 26 in Beijing?

Are there hotels inside the airport transit area or would we have to leave the airport?
Can you help us get a hotel for the night?

Thanks for all your help.

BK Blume