Welcome to the forums! To answer your questions

Is there a feature to multiply these onw fields, so that the author caon not only use them once, but serveral times

You can manage fields or a group of fields as an DataObject or perhaps as a Widget which can be shared over multiple pages depending on your use case.

For example if you had related objects to a page (object can relate to multiple pages and a page can have many objects) you can use a relationship to map the two. Have a read of tutorial 5 for an example on objects and relationships. If you have a more specific example I can provide code / documentation

it would be much better if I can build "global" contentfields which the author can include into a page himself

This is another type of content we added in the new 2.4 version. You can create global data fields on the SiteConfig panel and use them site wide. You would use this for instance to include pieces of text (header, sidebar, footer) that you used site wide and on every page.

is there a possibility, that the authot is able to choose data from an own database in the backend

So say you had a DataObject with the data (Name, Address) you would need 2 things. First: a way to add / edit / select these in the CMS. If you link to 1 at a time perhaps a HasOneComplexTableField would work well (refer to the tutorial 5 mentioned before for a guide).

The second thing you would need is a Controller to display the data. SSbits has a very good tutorial http://ssbits.com/using-silverstripe-url-parameters-to-display-dataobjects-on-a-page/ which would be of some help to you.

are there any special requirements fpr silverstripe

Make sure you read the server requirements page - http://doc.silverstripe.org/doku.php?id=server-requirements for any requirements. SilverStripe will work fine on many shared hosts but for the best experience I've found a VPS machine (or one you can have more control over) can give you an easier time.

whate about silverstripes performance

Every site is going to be different, 2.4 has several performance improvements and I've found it quite snappy even when working on overseas sites. Demo may have been slow for you depending on where in the world your located and the load on the server at the time.