I love tmux and I'm primarily a keyboard user. But sometimes I like to copy a short string from one window to another. Does tmux-yank allow you to middle-click paste on a tmux window? does it allow to select to copy?
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 :)
To get pasting from the system clipboard, you need something like https://github.com/brennanfee/tmux-paste It will copy whatever's on the system clipboard into tmux's paste buffer, and paste it, all with a single middle-click.
I've only recently started using tmux, and all this clipboard stuff was the biggest stumbling block. But I think I've got things work well enough now.