There is no certain time on how long it takes. Because the factors will always be different and the factors heavily affect the evaporation time. Some factors include: humidity, heat, how the sun is visible (whether clouds are covering it or not)
I believe d all of the above
Because of internal friction between layers of mud particles called viscosity. When you walk, your foot exerts a force on the mud; and according to Newton, the mud also (is supposed to) exert an equal opposite force, which leading to an equal net resultant force in your direction, propelling you forward.