I can offer a couple of suggestions. No guarantees.
As for the options window in Firefox, right click the connection in viewer, select properties, and under remote screen-additional properties, make sure "Capture Alpha-Blending Windows" is checked.
As for the mouse lag, I have this happening on an XP box that I maintain. The only solution that I have found, is to run Firefox with "Low" priority. To test this out, open task manager, find the Firefox process, right click on the process, select set priority, then select low. You can do this by starting Firefox with this shortcut, if the test has the desired result. This path is for an XP machine, you may have to edit it for Win 7.
%windir%\system32\cmd.exe /c cd "C:\Program Files\Mozilla Firefox" && start/low firefox
Hope this helps !!!