A lot of stuff loads on the WordPress backend and a lot of stuff happens when you edit things-- a lot more than happens on the front end of most websites. It could be that you are hitting a bandwidth limit or a connection timeout.
A lot of sites use PHP and MySQL, same as WordPress. That in itself shouldn't be an issue.
This is pretty interesting though:
I can even view the frontend of my sites unless dashboard is open in another tab.
I have never encountered that. Probably 90% of the time have a tab with the front end and another with the backend open at the same time. That could point to a cookie or session problem. It is going to be very hard to tell without carefully analyzing your traffic.
What kind of speed do you get with your connection? And it is consistent?
Sorry, all questions, no answers. I even had still another question but I can't remember it now :)
[Edit] Remembered my question :)
You said this started a year ago. Did you do anything just prior to the beginning of this issue? Add a plugin? Update the site? I know, I know... hard to remember.
Have you tried with all of you plugins disabled and using the defaout theme?