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Kickers copy, but things like "Entwine" and "Conspire" do not. If you copy a spell with Entwine, or perhaps pull one from a graveyard with Memory Plunder or the like, then you can opt to pay the Entwine if you have the ability to do so, but it won't be automatically paid for the copy even if it were paid for in the first casting.

Entwine will be copied and the copy will be entwined as well. Conspire is copied too, but like replicate it is in part a triggered ability that triggers on the spell being cast.

706.10. To copy a spell or activated ability means to put a copy of it onto the stack; a copy of a spell isn’t cast and a copy of an activated ability isn’t activated. A copy of a spell or ability copies both the characteristics of the spell or ability and all decisions made for it, including modes, targets, the
value of X, and additional or alternative costs. (See rule 601, "Casting Spells.") Choices that are normally made on resolution are not copied. If an effect of the copy refers to objects used to pay its costs, it uses the objects used to pay the costs of the original spell or ability. A copy of a spell is
owned by the player under whose control it was put on the stack. A copy of a spell or ability is controlled by the player under whose control it was put on the stack. A copy of a spell is itself a spell, even though it has no spell card associated with it. A copy of an ability is itself an ability.

That's good to know. Our group somehow came to the conclusion that Entwine wasn't copied when a spell with paid-Entwine is copied but the cost could be paid if able by the copy controller. Thanks for clearing that up for me, since I had it backwards this whole time!