Nexus 7 2013 has 4G support, but I can't find any information on 3G support. If I get a Nexus 7 4G model, can I use 3G?
The current New Nexus 7's only support wifi. They do not support any mobile data yet. But once they are released with mobile data support, you can count on them supporting older networks, like 3g (HSPA/HSPA+) as well as supporting 4g (LTE). LTE coverage is not wide enough for them to only support 4g.
Yes, it does support 2G (GSM/EDGE) and 3G (UMTS/HSPA+).
Source: https://support.google.com/nexus/answer/3248332
Nexus 7 (2013) Tech Specs (LTE)
North America and Japan:
GSM: 850/900/1800/1900 MHz
HSPA+: 850/900/1900/2100/AWS (1700/2100) MHz (Bands: 1/2/4/5/8)
LTE: 700/850/1700/1800/1900/2100 MHZ (Bands: 1/2/3/4/5/13/17)
Rest of World:
GSM: 850/900/1800/1900 MHz
HSPA+: 850/900/1900/2100/AWS (1700/2100) MHz (Bands: 1/2/4/5/8)
LTE: 800/850/1700/1800/1900/2100/2600 MHz (Bands: 1/2/3/4/5/7/20)
Note that it appears that there are two Nexus 7 2013 LTE models, which differ in LTE bands, but UMTS and GSM bands appear the same.