I installed the AMS module but I really don't understand where I can add articles. I'm planing to use it for articles of the writer's on my site. But so far I tried everything and it did not really work.

Since I couldn't do it with AMS I tried smartsection, there it was much easier. I created categories for writers and put their colums but with that module I couldn't put a block on the main page just with their pic and the first sentence from the article with "more" button...

So I couldn't get what I wanted from these two modules and the other modules seem either not working or can't be installed to my website..

What would you suggest, what I want is a view like this on the main page of my site:

click to view

Try the News module (http://xoops.instant-zero.com/) - you should be able to get something very close to that page using one of the News modules blocks on your top page.

The News module allows you to select articles by author.

Although it's called "News", it's a great module for managing articles and content too

Is it possible to import smartsection data into the news module?

AMS is a News clone and they are very similar.
For converting, if you copy your site to your home PC with a XAMPP server, then you could experiment with copying the databasetables as eg done in this French example for two fora (from NewBB/CBB to NewBBex).