If I shave does my facial hair grow back thicker and faster?

No. Hair is dead. It does not know if you are cutting it or not. Neither does your body. It is an old wives tale that started because when young boys became men and started shaving, their hair got thicker due to testosterone increases, not shaving. Short hair can feel stiffer but that is a mechanical issue, it just feels stiffer, it is not thicker.
No. This not true. If you are female it means something else is wrong.