Android - 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.

While your carrier wouldn't be able to directly detect you are using WiFi hotspot, they might notice that you are using a lot of data. This is often a red flag in their systems, and might get you a phone call and/or your bandwidth throttled/capped.

WiFi hotspot is not available on all devices. For instance, my og Droid with stock ROM doesn't offer this due to limitations artificially imposed by Verizon.

While a carrier cannot disable WiFi hotspot on a phone by phone basis, they most certainly can limit your bandwidth and/or cap it at a certain amount (for instance, I get full bandwith until I hit 2GB total, at which point it slows WAY down).