The answer to the first question: Because melting point and freezing point describe the same transition of matter, in this case from liquid to solid (freezing) or equivalently, from solid to liquid (melting).
2nd question: They do not take place simultaneously as for one you have to take energy in the form of heat out of water, this is called freezing and for other you need to give energy in the form of heat to ice, this is called melting. And they do not take place simultaneously as at a particular instant you can either supply energy or take it away from the system, so only one process takes place, unless you maintain a constant temperature of 0-degrees Celsius, where the ice and water are in state of dynamic equilibrium so here the molecules of water and ice interchange position from ice to water and from water to ice.