A free-body diagram shows one object and only the forces acting on it. Newton's first law says the velocity is constant when the resultant force is zero. The second law says the resultant force equals the rate of change of momentum, which becomes F = ma when the mass is constant. The third law says forces come in pairs: equal in size, opposite in direction, of the same type, and acting on two different objects.
Momentum (mass × velocity) is a vector. The total momentum of an isolated system is conserved in every collision and explosion. Kinetic energy is conserved only in an elastic collision.
An object moving in a circle at constant speed is accelerating towards the centre, so a resultant centripetal force must act towards the centre.