Dell XPS 13 L322X Ram Replacement

HI,

If you installed or replaced the memory modules, ensure that the memory modules are seated properly; otherwise you may get a 2 beep code. If you get a 2 or 4 beep code please test one memory module at the time if possible.

This is the Error code Description for all beep.

1) You can attempt to add a single 8GB module but you will not get dual channel function natively doing that (if it works)
2) I will suggest sticking with Dell's recommendation of 8GB (2x4GB) which is what I would suggest as an upgrade (purchased as a dual channel kit)
3) Although you can run 1600MHz ram (Corsair Memory Finder Tool even links to a 1600MHz kit), you will not be able to get 1600MHz throughput. You would not be able to run in dual channel if adding ram of a different frequency

The memory on this model is soldered to the mainboard - when it fails, the system board needs to be replaced (it's not removeable and there is no socket for adding RAM to the system).

Oh great, that sounds expensive because of some terrible design by DELL I get punished. 

It's an increasingly common design that started with Apple - though at least Dell hasn't resorted to soldering in the solid state drive (as Apple has on many of its newer systems).