Microsoft
MicrosoftRegarding invalid SSL certs impacting authentication -- SSL cert exchange happens before HTTP, and they generally do not affect each other. If something happens during SSL cert exchange and HTTP doesn't happen, then Windows Auth won't happen either.
If you're referring to mutual TLS, where the client also sends a certificate to the server, then the server can use that cert for auth (if configured) and the auth flow described in this blog doesn't happen, since the user was authenticated via the cert. There are other things that can happen here, such as the client cert being invalid, that can affect and alter the flow of things, so if you have a more specific question on that feel free to ask.
Regarding the .NET assemblies question, I am not sure what you mean here. For ASP.NET specifically, the setting of the HttpContext user happens on the native side when the managed objects are being built-out and their properties mapped. I have never seen a problem with specific assembly versions not picking anything up here, as this code is quite stable. If you have something more specific feel free to ask.