Liquid paraffin is a highly refined mineral oil. In other words, it is a stable, long-chain hydrocarbon. There will be NO chemical changes doing any of the things you suggest in moderation.
1.
If you were to reduce the temperature, it would first become thicker like Vaseline and then set something like candle wax. Physical changes, but not chemical changes.
2.
If you were to heat it in a microwave, it would get hotter and more fluid. If you continued to heat it, it would turn to vapour where it would become a fire risk. If it were to catch alight, then yes, chemical changes would occur as it combined with oxygen from the air to form water and carbon dioxide.
3.
What do you mean by 'Dry'? There is no water in liquid paraffin, so no, you cannot dry it. I wouldn't recommend trying to fry with it either as much cheaper and more suitable alternatives are available. In any case, the body cannot digest Liquid Paraffin so it would act as a laxative.