1: The latest patches has helped a lot with this. All the most used popups now close properly, but there are still a few (mostly error Messages) that has to be closed by pointing and clicking.
2: You still got to close first, but as esc closes its no big deal anymore.
3: TDM modpack will improve the AI beyond recognition. Give them a bonus and they will be quite a handfull. Diplomacy is still not their strong side though, so if you want diplomacy; play against humans.
4: The ministers in SEIV are closely modelled by RL politician/civil servants. If you want the job done properly, do it yourself.
As a carpal tunnel syndrome sufferer, I can symphathise with your consern about to much mousework. Even if the UI has more mousework than stricktly neccessary it is no problem for me to play this game (a lot). Features like waypoints, copying building queues, all the hotkeys (like space for moving through the ships available for orders), and Multi-adding both reduces and breaks up the workload, giving the neccessary rest to the mouse hand.