External GPU & Monitor Support for the XPS 13 7390 (Not 2-in-1)

If you want to run all of that hardware, your best bet would be an eGPU enclosure that itself provided power to the attached system (the XPS 13 requires 45W for proper functioning) and also had built-in USB ports that you could plug your other peripherals into.  The only other way to do it while maintaining a single cable connection to your PC would be to connect the system to a Thunderbolt 3 docking station that supplied power and included an "upstream" Thunderbolt 3 port for peripherals, and then connect your eGPU to that port on the dock -- but that would be more expensive overall, and considering that you'd presumably be attaching any external displays to the eGPU itself, then most of the dock's functionality would be useless to you.

To the question about PCIe lanes, I believe the answer is x4, but I'm trying to track down an official source there.  As for eGPU compatibility, considering that older systems have been able to run an eGPU, I don't see why you'd have a problem there.  If you haven't already, eGPU.io and its forums are a useful resource for learning about experiences people have with various systems, and as the name implies, it's focused around eGPU setups and therefore has some people very knowledgeable about that subject available.  One thing to be aware of though is that the XPS 13 models use Intel's low power U Series CPUs, not the higher performance H Series CPUs used in models like the XPS 15.  As a result, high-end GPUs could become bottlenecked by that system's CPU, so you may find that money spent getting the top-end GPU would be wasted.  Just fyi.