In which market structures does the producer employ price discrimination?
Market power required for price-discrimination?

In my understanding, no. I'm pretty sure that one can show this mathematically, but I'll just give you the intuition. Price-discrimination (PD) increases profits, because it incorporates different price-elasticities by having different prices. Therefore, a firm that incorporates PD should make, c.p. more profits than a firm that does not.

Perfect competition means that less profitable firms are forced out of the market. In this case, perfect competition will lead to firms that act with price-discrimination whenever they can.

Think about restaurants, where there is a lot of price-discrimination going on, either via lunch offers or menu pricing. Restaurants really shouldn't have market power, should they?