Replacing Crankset. Do I need to replace chain? Then do I need to replace cassette?
If you replace the crankset you almost certainly get new front sprockets.  Compared to the cost of the crankset and sprockets a new chain is chicken feed, so get a new chain.

Whether you need to replace the rear cassette is a whole 'nother question, pretty much independent from the front.  If the cassette is badly worn it may cause your chain to wear slightly faster, but not enough to worry about.  And you may find that the rear shifts poorly with the new chain, or suffers some "chain suck", but probably it will be OK, if it is now.