In an elastic collision of two billiard balls

Answer carefully with reasons
(i) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls i. e. when they are in contact?
(ii) Is the total linear momentum conserved during the short time of an elastic collision of two balls?

(iii) What are the answer to (i) and (ii) for an inelastic collision?
(iv) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note: We are talking here of potential energy corresponding to the force during collision, not gravitational potential energy.)

(i) No, the total kinetic energy, does not remain conserved during the short time when two billiard balls are in contact. At that time, balls are at rest and their KE is zero. In fact, all this KE has been transformed into elastic potential energy of balls.
(ii) Yes, total linear momentum remains conserved during the short time of an elastic collision of two balls. The balls exert forces on one another due to which individual momenta of two balls change but total linear momentum remains conserved.
(iii) For an inelastic, collision kinetic energy is not
conserved but total linear momentum is conserved even now.
(iv) As the potential energy depends only on the
separation distance between the centres of balls, it means that conservative forces are in action (because PE changes due to conservative forces only). Hence, collision is surely inelastic collision.