This explains the Adsense warning because the server-side part of the framework used (gwt) is seeing a different user agent than what the client part is seeing.
Granted, UA sniffing is bad practice on either client or server side, but if you do it and send content tailored for browser A and then see that, strangely, the client is actually browser B, then you are probably allowed to be confused and complain (better than failing in strange ways).
Also knowing that, it's unlikely that something on the server side is causing these connection reset issues because, as I just said: the server still sees a chrome user agent and producing a connection reset error (RST packet) requires connection level involvement (server or somewhere in between, but never the client browser, minus bugs).
In general: be very careful what error messages you see: the Adsense error is different from the gmail error which in turn is (likely) different from the connection reset issue.
Overall there is too much conflicting information to attribute malice or even just intent to Google here.
If I were in that users position, I'd check my firewall and/or proxy configuration (and try disabling HTTP pipelining if it's active in Firefox - it's disabled by default for a reason) as the problem is much more likely somewhere over there.