QIf I play a card from my cemetery for 0 play points with Hina Araki's On Evolve ability, will this follower's ability trigger?

AYes. It triggers regardless of the zone from which you play the card. Note that you can also technically "play" abilities, but this follower's ability only triggers when you play a card.

QWill playing this follower trigger its own ability?

ANo, it won't. Unless otherwise stated, cards have to be on the field before their abilities come into effect.