You should start by reading the following Technotes, some of this you have found out during your testing Sametime WebPlayer (Browser) plugin Install window keeps loading for a long time in Internet Explorer browser and the yellow bar never displays
and User not able to join Audio Video conferencing from Sametime Meetings or User not able to perform ScreenCapture from Sametime WebChat.
IBM state that 64 bit browsers are not supported, see here
I think it is best that Chrome is avoided, as the changed Google have made means that they do not allow the plugin to run any more so screen sharing and A/V is not possible.
I have run into a few installations now using Windows 7 PCs that do not automatically install the plugin due to UAC. This makes it difficult to deploy the plugin without using some kind of deployment software which is no good for external users joining the meeting.
Chrome - Prompts to install plugin, I try this, it downloads but then Chrome says that "Applications are not allowed to be installed from this site"
This is probably due to the changes Google made.
Chrome (seems to be 32bit) does not prompt for any plugin. But when I try to do screenshare I asks to install Java.
Probably the same answer as above.
Windows 10 is not listed in the supported OS
The new fix available on Fix Central for the Connect and embedded clients has support for Windows 10 but I cannot find any other mention to Windows 10 http://www-01.ibm.com/support/docview.wss?uid=swg21965392
It may be worth you raising a PMR to ask IBM directly.