Middle-click I don't know about, as I never use it. Usually I don't even have a mouse connected to my computer so I'm limited to a keyboard only. I use the provided `yank` (prefix+y by default) to copy and normal ctrl+shift+v to paste in terminal. Then in other applications I just use ctrl+v and ctrl+c normally.
For the "select to copy", all the information you need is in the GitHub repository previously linked. Here it is again: https://github.com/tmux-plugins/tmux-yank The specific section you're looking for is here: https://github.com/tmux-plugins/tmux-yank#mouse-support
It's simple for you to try it out as well, have a read about tmux plugins and you'll be up and running in a yiffy.
Also take some time to read up on terminal emulators, shells and what tmux is, as you seem to hold slightly off assumptions around where the problems you're experiencing are actually coming from. The reading and understanding will only make your personal knowledge base larger and deeper :)