The fact that a engine is not overheating, but the warning horn sounds off with a constant steady beep, and that the rpms drop drastically would indicate that the engine is starving for fuel due to a fuel restriction. Check the built in fuel tank where the rubber fuel line attaches to the tank fitting. That fitting is in all probability a "Anti Siphon" valve which is notorious for sticking in a semi closed position. It will be aluminum, about 2" long, and the insides of it will consist of a spring, a ball, and a ball seat. If this valve exists, remove it, knock out those inner components which will convert it to a straight through fitting, then re-install it. Hopefully that cures the problem. more