First off, if your engine only has a few runs on it, it's nowhere near broken-in. It will take over a gallon's worth of running for the engine to come in, starting out rich and working towards peak RPM.

Fuel will drip somewhat from the carb, especially at the lower throttle settings when muffler pressure is used. That happens with an updraft carburetor.

Holding the model nose down will cause the engine to go rich and then quit. It goes rich because gravity pulling down will increase the fuel pressure a bit. It will quit because the fuel pickup will become unported and you basically run out of fuel for the engine, as the fuel line draws only air.

As far as temperatures go, it's normal to the engine to get hot enough to cause a nasty burn. We don't worry at all about engine temps. We consider the RPM the engine's running, how it handles, and how it sounds. We never monitor temperatures, so we don't have any to give you.

Basically, as long as the engine's running rich of peak RPM and is handling well, and you're using a good-quality fuel, the temps will take care of themselves, assuming proper airflow to cool the engine...and this will be borne out in the handling.