QIf I put a follower from my hand onto my field with this amulet's activated ability and then evolve it, do I still have to destroy it at the start of my end phase?

AYes, you do.

QIf I put Lucifer from my hand onto my field with this amulet's activated ability, do I still give my leader +4 defense at the start of my end phase?

AYes. The "At the start of your end phase, destroy this card" ability given to Lucifer by this amulet and Lucifer's "At the start of your end phase, give your leader +4 defense" ability both trigger and become pending at the same time. You can then choose the order in which you resolve them.