Is that possible that ue will always open the same content browser for every material, texture, WHATEVER?
You could save everything into the “engine” folder -> then you will have access to all files in all projects 
C/Programs/UnrealEngine/4.7/Engine/Content
i think you missed the point.
If you open new material, you wont have content browser in that window.
I would like the content browser to be opened with anything, be it material or blueprint,
just global always available window of content browser.
Oh, yep, sorry -> go to window - content browser - enable “content browser 2”. Now you should have a window that you can place somewhere on your screen (or your 2nd monitor) -> as far as I know it should stay open all the time
Ok now you can put that second content browser somewhere, like in some material, but as soon as you open another one, its gone.
And second monitor is not an option
tl:dr i obviously tried that and its not an answer
Dont put it into a material or any other “window slot”, just leave it open and place it on the right side of the screen, then it will always stay open 
Question is still open if its impossible to keep 1 content browser opened at all times ill create a feature request.
As I mentioned above, yes -> go to window - content browser - enable “content browser 2”.