Normally they're mounted on the exhaust headers just downstream of the port. Usually these would only be mounted when the engine is under test on a dyno, drag engines might have them always mounted.

Normally oxygen sensors are mounted on the collectors before the catalyst. If you run the engine too rich (ie too much fuel) the catalyst works too well and can melt down, conversely if you run the engine too lean(not enough fuel), the exhaust gas temperature rises and can melt the catalyst amongst other things.

Generally EGT is more critical on two stroke engines - if you ever see a gokart race where the guys tweak their mixture at the end of the straight. They have a EGT meter where they try to run lean as possible for maximum power (this is the opposite for a 4 stroek motor) and richen up for drive out of the corners.