Track pad and plug-in mouse left click not working
I would recommend splitting this question in 2 since you had 2 different issues even though they are affecting each other. 


First one (this post) would be to only figure out how to reinstall OS with just keyboard. Take some pictures with your phone and post them along with your question so we can help you better. 
If your input hardware doesn't work even after the OS re-install, post your second question with the new post-OS-install details.


As for your hardware, have you tried using tab and shift + tab to change focus (indicated with a blue boundary) and use spacebar to select that button, while enter only works for the button filled entirely with blue colour.