What theme are you using? Do any of the blocks have custom templates?

Its possible a theme or custom block template is inadvertently interfering with the dashboard.

You could experiment with switching to elemental and see if solves the edit problem. Some page areas may disappear, but they will reappear when you switch back again.

Also look in your browser developer console and see if there are any JavaScript errors. Faulty JavaScript could be preventing edit mode from working fully.

I use the theme Anitya. The developer Console shows this error:

Uncaught TypeError: Cannot read property 'replace' of undefined
at Function.x.template (underscore.js:1)
at x.(/anonymous function) [as template] (http://aveska.w-h.net/updates/concrete5-8.2.1_remote_updater/concrete/js/underscore.js:1:12613)
at d.Area.init (app.js:7)
at new d.Area (app.js:7)
at HTMLDivElement.<anonymous> (app.js:6)
at Function.each (jquery.js:2)
at m.fn.init.each (jquery.js:2)
at d.EditMode.scanBlocks (app.js:6)
at d.EditMode.init (app.js:6)
at new d.EditMode (app.js:6)

the last change was to link the logo on the home page and to delete the "index.php" in the url

I really don't know what i have to do to fix this.

There is a good chance the script error is the root of your troubles. At a guess (and it could be something else), the problem could arise from an incomplete upgrade of c5 or that the theme is not compatible with your current core version.

First, I would experiment with swapping to the default elemental theme. If edit then works, you know it is a theme issue.

What version did you last update from? If you took a backup from before the problems started, you could revert to the backup.

Otherwise, you will need someone with experience, knowledge and time to dig into it.

I would say it a theme issue. While developing themes I sometimes get this condition and I strip out the css to finally identify the selector that's causing the issue.