Sorry for the issues you've had with that system. The driver you've installed is Version 1.555.0.0, A02, correct?
Check out this article and see if it can help you out:
Since the Dell 1820a can handle both 2.4 GHz and 5.0 GHz bandwidth have you tried connecting on the 5.0 band to see how the connection is with that? The system might be getting too much interference at the 2.4 GHz range and may work better for you on the 5.0 band.
Also, try turning off bluetooth as a test and see if that helps improve your connection speed and quality.
You said it's having connection issues with all networks. Could it be that the antenna leads have worked loose during shipping? Here is a link to the XPS 13 9350 Service Manual showing how to check the antenna connection.
Try the resolving connection issues link above and let me know if changing the connection to the 5.0 GHz works better, as well as whether turning off bluetooth helps. And if you can check the antenna leads to make sure they're snug. To better help me troubleshoot this problem please click on my Dell Todd username and send me a private message with the Dell Service Tag of the system. Please keep discussions about troubleshoot and steps taken here in this thread so others, who might have the same problems, can see what is done to resolve the issue.