How can I create a subdomain, for instance sub.domain.com that would go to the redirect path and without changing the url (w/o redirecting)?
Yeah, but that way its not a subdomain anymore its a domain... it uses new quota and everything ... developers really need to fix this.
If the url in the address bar of the browser changes or not depends on the rewrite mode that you use and if you use a rewrite to a directory or a url. If you like to know how the different rewrite modes of apache work, please see apache rewrite guide in the apache documentation. But in general you should create a new website if a subdomain shall have its own directory as dclardy explained, thats described in the manual as well.