Installing Fiddler's root certificate will not help with certificate name mismatch errors. When you use iptables to reroute Android traffic, you need to set the SetCNFromSNI preference: https://groups.google.com/d/msg/httpfiddler/hvsDR14j1Lg/P02zBzIYCE4J
so that Fiddler knows what server it's talking to (rather than just its IP address).
In the other scenario, where you don't even see a CONNECT request, this is a sign that there's a bug somewhere in the client application or your jailbreaking/trustbreaking software, since Fiddler obviously can't screw anything up if you're not even sending it traffic. :-)
Check out the Telerik Platform - the only platform that combines a rich set of UI tools with powerful cloud services to develop web, hybrid and native mobile apps.