I want to know is there is a possibility to build a code/script etc. (never mind in which programming language) that will do the next thing. for instance, if my main domain is www.alex.com, so when I go to www.alex.com/**xxxyyyzzz** it will generate automatically a web page with some information (templete for all of the non-existing pages?) even if there is no "xxxyyyzzz" in the database? In other words I need some kind of page generator when sub link is being requested.
Have you heard about frameworks?
A framework can do what you are looking for. Depending on the url, they can generate your page.
Here is a great one - codeigniter
Another one - yii.