TLDR; This issue has been partially tracked down, and it seems to be network-related. It went away when using a mobile hotspot, but so far I am not aware of any final solution.
In order to (hopefully) help others with the same issue I have provided my conclusion sent to @SuitedHound below.
There is an issue with your network setup ( Error: unable to verify the first certificate ). There could be many reasons for this, it is impossible for me/us to tell you the exact cause.
Basically, the error indicates that it tried and failed to verify the first certificate in a small chain of certificates. These certificates are used to encrypt your traffic, and verifying them is crucial to ensure the authenticity of both you/your request and our servers.
We have double-checked our own certificates and everything is green on our side. Your computer, or rather some software on it, is intercepting network traffic in a way that is not compatible with our security standards. A likely scenario is that some antivirus or “network security” software is adding a certificate to the chain in an attempt to make the connection more secure, crippling the security in the process 
The “Proxies” section in this post describes possible scenarios and solutions. Please have a look there and see if any of it helps!