Two part question: 1, if I put a bottle of methanol fuel additive in a gas tank that is less than full, will..?

Methanol is only harmful to engines if you let it sit on the engine components because it is a type of alcohol that attacks and corrodes metal parts unless it is burned. Since your gasoline engine was not designed to run this fuel, it will get harmed overtime. Methanol is primarily used on specialized engines. Though i'm not clear on the procedures for car sized engines, rc/nitro engines needs to be cleaned after every use with WD-40, etc so the alcohol does not harm the engine. Also, it is not as flammable as gasoline.