Well, it's slightly better than driving it without oil, or with a time bomb strapped to the engine, but no, it's not "okay".
drive it without coolant
.
4 miles in winter2 miles in summer
Not for very long, the coolant will splash out to a point where it will overheat.
No since you might collide with something or someone else
It is a very bad idea to drive a car without coolant. You will overheat your motor and risk warping or cracking your head(s) and blowing your head gasket. It's also not good for water pumps to operate without coolant in the system. If it's an old Volkswagen, as long as you like (VW bugs had air-cooled engines).
It will seize - due lack of lubrication and coolant (one of the oil's uses)
If it is in the winter make sure the radiator is full of water with antifreeze before starting the car. If this leak is not too severe it should be ok to drive a couple of miles to a mechanic.
You can not, and should not drive a car that has a bad water pump. The water pump pumps coolant through the engine. You engine will overheat and die without a functioning water pump.
No! It is illegal to drive a car without a licence.
If it's stuck open, yes you can. If it's stuck close, no you cannot drive the car.
Nobody could answer that question without looking at your car. One of the possibilities is that your car is overheating. Check the coolant. By the way, if this is the case, and you are driving your car without coolant, stop driving right now because your car is in danger of being irreversabely ruined forever.