Basically your problem is you took all the child portal folders and put them in the childs subfolder.   When you make a request of /portal.com/child1, it will look for the 'default.aspx' file that is placed into the child portal subfolder when you create the child portal.    THis is because IIS will append /default.aspx to the end of a 'path' url, in accordance with the 'default document' setting in your IIS configuration.  If you break this relationship between the Urls and the physical folder structure on the web server, IIS doesn't know how to resolve the request properly, and you get the 404 error.  Adding the /default.aspx on the end (manually) kind of gets around the problem, but not correctly as you have found out.

My advice is to return all the child portals to the website root directory out of the /childs directory.  It might look a little messy but your sites should start working again.

To answer your other question, it is possible to get the pagename of the home tab appearing - just change your site settings so that there is no home page specified.  The Friendly Url Provider will then generate the /home.aspx url for the 'home' page of the site.