If you sell merch, does epic take 5% cut?

Unreal engine requires 5% cut of all revenues.

If I sell merch that uses none of the game engine obviously, just the characters world and other copyright belonging to us, do they get a 5% cut?

No, you do not owe royalties on merchandise related to your game, unless the merchandise contains functionality that ties in with the operation of your game.

However, no royalty is owed on the
following forms of revenue:

  1. Revenue from ancillary products which are not software and which do
    not contain embedded information (such
    as QR codes) which affects the
    operation of the Product (e.g., comic
    books, soundtracks, apparel);