It is possible, but usually not desired. If you have included URL in the index then a search for http might work. Otherwise to use REX you would need to enable that on the search settings page, and a search for /. would work.
From the administrative interface you can use List/Edit Urls to get a list of all the URLs in the index.
Yes, allow linear. If you do a search in the Test Mode it should show you error messages which indicate why a query is not performed. You should not generally enable allow linear for public searches as they can take a lot longer to perform.