That's conservation of angular momentum and the only time that needs to be worried about is with a helicopter doing an auto-rotate. But I'll keep it in mind if I ever use a bar stool to spin a prop

Diameter of a prop has more to do with thrust than anything else, or more correctly the area the prop disc covers. This area is the column of air that gets accelerated by the prop. If you go from a 10" prop to an 11" then the diameter goes up 10% but the area the prop sweeps out goes up by the square (or 21%). This takes more HP so if the engine is nearing its limit you have to reduce the pitch to reduce the load.