Electrical – Does an outdoor outlet mounted on a patio ceiling require protection from a GFCI

Neutrals shouldn't be connected together with the GFCI. Connect the neutral of the line and load to the appropriate connections on each side of the GFCI. Otherwise, the current will appear to go out via the hot connection and not return via the neutral on the load side of the connection, which is exactly the scenario that the GFCI detects and trips on.

Also, note this important tip from Shirlock, use the push in connectors for the GFCI outlets: When to use holes instead of side terminals to wire an outlet

The first problem can be dealt with using a Bell 5403 or equivalent weatherproof extension box to provide a place to hook the conduit to and some extra cubic inches for the additional wire fill. You'll need to hook a ground pigtail to it, by the way -- there do not seem to be non-metallic weatherproof extension boxes.

Since you are running conduit under the deck -- you can run individual THWN wires inside it instead of a UF cable (although running UF aboveground is permitted when protected from physical damage and direct sunlight if it isn't IDed as sunlight resistant), and running THWN will make it easier to pull even with an oversized conduit -- 3/4" inch will provide ample space for a single circuit extension like yours. Don't forget to put in expansion fittings, lest your conduit run do the snake on you!

Last but not least -- simply use an ordinary outlet for the new outlet, and run it from the LOAD terminals on the existing GFCI. (Although putting two GFCIs in series won't break anything, it could confuse you as there is no guarantee as to which one will trip when something happens.)