Stinky air when I turn on the bathroom faucet...what is causing it?
I think what you've got is a blocked vent pipe, or worse, a non-existant or improperly-installed vent pipe. The vent pipe is supposed to connect to from the waste pipe stack or top of a lavatory drain pipe up through the roof, and is there to equalize plumbing system pressure and provide a means for sewer gas to escape. If the vent pipe is blocked, then the water flowing from the sink will increase the air pressure in the waste pipes, possible forcing sewer gas through the toilet trap out into the bathroom. 

Check your vent pipes to make sure they're clear and hooked up properly. The article here might be useful http://bradyinspects.com/plumbing-vents