If you do not want to register your own domain, is it possible to get an address of the type http://www.space2u.com/~username/?

No, this kind of local paths are not available. If you do not want to register an own domain, it is possible to without cost (for the domain, the web hotel fees are ofcourse still there) use a subdomain to space2u.com, for example http://yourchoice.space2u.com/

Answer "Yes" on the question if the domain is already registered and then fill in your wanted subdomain (in the order form).