Question

Does Centripetal force ALWAYS = (static coefficient)*(Normal Force)?

Answer 1

I'm thinking you mean the frictional force?

Centripetal is: \[F_{cp} = (mv^2)/r\]
where m is mass, v is speed, r is distance from center.

Frictional force is \[F_{fr} = \mu * N\]
But that is the maximum frictional force.

The actual frictional force is the same as the force that wants to move the object as long as the moving force is less then the maximum frictional force.
So if you have someone pushing an object (lets say a brick on a table) with 3N and the maximum frictional force (static coefficient * Normal Force) is 5N, the actual frictional force is going to be exactly 3N in the opposite direction of the pushing force so that it cancels it. This has to be the case or else the object would move.
If the pushing force is increased to 7N then the frictional force would be the maximum it can be, 5N, and there would be a total net force on the object of 2N in the direction of pushing and the object would move.

One more thing to add is that most materials have a static coefficient which tells how hard it is to move an object when it is standing still, and a dynamic coefficient which tell how hard it is to keep pushing the object when it is already moving. These two are usually different with the static coefficient being larger, that is to say, it is harder to get some object moving then it is to keep it moving.