Hello,
sorry for my english - it is not so good.

After the installation i get the following error in backend and frontend:
Fatal error: Call to undefined function curl_init() in /users/voelkerfamilie/www/ImpressPages/index.php on line 105
see here:
http://voelkerfamilie.bplaced.net/ImpressPages/

Any ideas? What is the reason and what can i do?
My only modification is the deactivation of htaccess in the root-directory. Without this i can not run the installation.

Activate/install the php extension: php_curl - and it will work.

I also received this message when I installed impresspages on my wamp server because wamp doesn't have it as default.

We know this issue. Curl required for fake cron. In future system will check if your server have installed curl. And if no, fake cron will be turned off. But then you will need to configure a real cron through control panel or unix console.

A file yoursite.com/cron.php should be executed about once a day for maintenance.

Ok, i will ask my provider for installation or activation of "php_curl".
It's not so easy, because my Hoster is a Freewebspace-Provider. My normal Provider
don't support php-version 5.3 So i decided to go to the only (free)-Provider with php 5.3 i can find.
What is the reason to execute cron.php once a day? For maintenance? Is it for database reorganisation?
Please give me a workarround to deaktivate fake cron.

Cron is used for many tasks:

delete old temporary files
delete old logs
create statistics for sitemap (how often the pages are changed)
send emails from queue

And you did't need any workaround. Simply setup a cron in any way you like. The easiest one is every day point your browser to yoursite.com/cron.php But you might find a better ways.

To turn off the fake cron, go to Developer -> Modules config -> configuration -> Advanced Options -> Use fake cron and clear the check box.

If the website is not very important, you can run a cron only once at a week. Might be the most important thing, the cron does is sending of emails. But if you don't use the newsletter or there is not a lot of emails at once (hundreds), then the cron is not a critical thing.

Good luck.