RE: XPS 13 9350 docking station compatibility
Figured I'd help you out here, as we also purchased the Dell 13 9350's with the D3100 docking stations. The docking stations do work and are the suggested docks to use with the 9350, according to the rep at Dell I spoke with when I originally ordered the laptops. I've also had to troubleshoot the 2nd issue quite frequently here.
Unfortunately for your first issue, Dell does not make conventional docking stations for these laptops. They should really be classified as Port Replicators, because that is all they are. Any "docking station" you purchase for this laptop WILL NOT charge it. It is the same with the 12's and 15's, so pretty sure it is like this with all XPS laptops.
As for the intermittent issues, we use Windows 8/8.1, most of the time the issue is due to the USB ports timing out, which is common with Windows 8/8.1. Simply locking the laptop (Windows Key + L) will fix the issue if this is the problem. However, I'd also suggest updating the drivers on the dock, as that did help alleviate some of the issues we experienced. Here is the link: