Kozmopolip

Yes — you must always move Cosmoctopus to an orthogonally adjacent tile on your turn and you only gain the bonus of the final tile you land on; you may spend one resource per extra tile as Tribute to move further but you cannot return to the tile you started on. (page 4) Also, Tribute must be paid with resources, not by discarding cards. (page 15)

Yes — you may discard any number of cards to discount a card: discarding a Scripture/Relic/Hallucination/Constellation gives a 1-of-that-type discount, and you may discard cards of any type to discount a generic (diamond) cost; you may also discard cards to discount Forbidden Knowledge. (page 5, page 15)

Colored Scripture discounts (black/gold/red/green) apply only to matching resource costs and may be used against Forbidden Knowledge of that type, while diamond (generic) Scripture discounts apply only to diamond costs and cannot be used against Forbidden Knowledge unless the Scripture specifically has the Forbidden Scripture icon. (page 6, page 8)

At the end of your turn you must discard until you have at most 8 cards in hand and at most 8 of any single resource type. (page 8)

No — you cannot fill constellation slots with resources you gained before the constellation was played; you must place resources you gain after playing the constellation, and you must start with the top-left slot (A). (page 7, page 15)