Of course installing 3rd party browsers in WINE won't make any difference. If you can install/browse with them, that's because they will use 3rd party libraries like OpenSSL and have their own certificate stores which have no dependences on the underlying APIs provided by the OS.I only try to used it to open links, didn't expect that solved the conection issues
All internet connectivity in JScript Panel and Spider Monkey Panel is through the xmlhttp ActiveXObject / built in windows certificate store which is entirely dependent on how updated the OS is. It doesn't necessarily have to be that way but that's the way all scripts are currently written. No one has gone out of their way with alternatives because no one cares about WINE enough.
I understand this, the program is for windows and is must be more convenient use the already existing tools of the OS.
It will be cool if it was different but linux users are a minority.
Until then the only thing that left is wait for a implementation in the wine side.