Does a carrier know I am tethering via Wifi Hotspot?
It is not detectable, but using tethering on Android with an second device leaves a lot of traces:


User-Agent Headers within HTTP that come from non-mobile browser
Increased Traffic consumption
Connection to services that are not available on Android/Smartphone devices (e.g. World of Warcraft)


and many more I can't think of atm.

But I have never heard of a carrier that goes for a trial, even if it's a violation of services from most carrier contracts. IMHO Mobile carriers have other problems at the moment, like overall increased mobile data traffic because of the smartphone boom. These is currently handled by soft limits of data traffic, that when reached only allow traffic over 2G connections. 
Or, to answer your second question, if you buy a smartphone from some carriers, the build in tethering function is locked and not usable.