Is there a way to open certain tree structure when people belonging to certain group logs into the admin panel?
Not out of the box, you could add something on your home page controller which is the first node that you hit when loggin in to the CMS that redirects the user to another page if they are in a certain group and in PageEditing mode. If they are in the CMS and you go through the URL resolver that will keep them in the CMS and the editor UI will expand the tree to the redirected page. You'd have to make it so it only happens the first time maybe be saving a session value or a cookie or something but it wouldn't be hard to implement. I would suggest setting the pages in a settings node on your home page or configuration node.