Yes.

Public Key encryption (or asymmetric encryption) requires a pair of keys; a public and a private key for exchanging data in a secure manner.

PKI must use asymmetric encryption because it is managing the keys in many cases. This implies the use of public and private key pairs, which is asymmetric.

Mostly for performance - symmetric encryption is much much faster (order of magnitudes) than asymmetric encryption.

Mostly for performance - symmetric encryption is much much faster (order of magnitudes) than asymmetric encryption.

Yes