If I got a Silverstripe Site in the subfolder on the server (eg. www.mydomain.com/mysilverstripesite), and all links automatically started with this www.mydomain.com/mysilverstripesite (www.mydomain.com/mysilverstripesite/myhome, www.mydomain.com/mysilverstripesite/mygallery etc)
and now if I want to move all this files, for example to public_html folder to have the access to the site with simply www.mydomain.com, than what should I change, and where ( if should something to be changed ) to get the url like
(www.mydomain.com/myhome, www.mydomain.com/mygallery etc
Silverstripe is URL independent. Its not like a system like Wordpress where you have hardcoded URLs in the database or a config file. As long as you haven't used any absolute URL's in your content area or your theme/classes, you should be fine to transfer your sites location.
As part of our development process, I regularly have one Silverstripe project in 3 or 4 locations, if it wasn't URL independant, I would have a nightmare moving between locations :s.