A Question About Payment

One, and this kinda feels silly to ask but, am I allowed to use Ue4 for something like this?

Yes!

And two, seeing how it’s a one time request and I’ll be paid once for a single copy, how would I go about giving Epic games their cut?

You have a couple options here.

  1. You can distribute under the standard EULA, where you’ll owe 5% royalties to Epic. However, you do not owe any royalties for the first $3,000 (every quarter). Under this model, you can sell your product to others, including to the general public.
  2. You can distribute under the Studio EULA for free (i.e., no royalties owed to Epic). Under this model, you can only sell to a single third party. Since it sounds like you’re doing a custom job for a single client, this may work for you.

Either way, you should review the EULAs carefully. If you want more specifics on the mechanics of payment, check out this page.