I want to change the url in every title post. If you now click on the title, you get the permalink. I want to change that in a custom url:

So:
<a href="http://wordpress-domain.com/?p=19" rel="bookmark" title="Permanent Link to Beste site">TITLE/a>

Would be:
<a href="http://custom-domain.com" rel="bookmark" title="title">TITLE/a>

AND

I want to add a screenshot like this:
<img src="http://grabber.developertool.net/Screenshot.ashx?u=www.custom-domain.com" />

the only place you can change teh permalinks is at dashboard->settings->permalinks AND the smae stule will apply to all posts. This is a WORDPRESS restriction. The post title is the link to the post itself. Let's say you have an archives page that displays th epost titles. The title will be the link to the post.

Even if you could change it and didn't care about messing up the internal links that wordpress uses, you would have to put in some code to test the post ID then change the link for every post - go and edit the code to add a new link - a lot of ongoing work AND when you updated, you would have to do it all over.

So unless the premalink structure fits your needs, I would change your idea of what you are trying to do.

Well I dont have to go into the post! So I dont need that link anymore...
Every title must go to a external website, not the single post page itself

That's not how Wordpress works. You could change it, but for EVERY POST you will have to add logic to the theme to assign a hard coded link and when you update the theme you will add teh code back in.

It might be possible to build a plugin that would add a feild to the post editior that would be your new 'link' and then it would grab that field when WordPress is giving the theme the link. But that is way beyond this forum. If you don't have the skills to do that kind of plugin coding, you will have to hire someone to do it. (For what it's worth, I give it a rough estimate of 20-40 hours coding and testing)

Why use the post titles? why not just create a page and hard code the link to what you would have used as the post title?

Because I use Gravityforms and there the visitor can send a url. This domain will be send to the database and that will be replaced where normally the permalink would be...

So every post will get his own domain.

This is a site with the same post I would like to have:
http://advertentiewebsites.nl/#gf_2

so why not use CSS to hide the post title and then in each post add a link as the first line?