WordPress 4.4.7 – update notworking

[ Moderator note: moved to Fixing WordPress. ]

I have for some while been unable to install new plugins – or even updates old one. When trying to install new plugins, a blank site appear that the page cannot be found no matter what I try.
If I try to update existing plugin it just keep on spinning arround and nothing happends

So thought a update to the latest version would fix the problem. But when clicking on the “update now” a blank screen does just appear

Anyone has any suggestion what to do ? Should I install it manually or ?
Is it just a default site I have, nothing fancy – Autoupdate has been working before