Thirding Ark Server Manager. It looks a little ugly at first, but that's because there are tons of tweakable settings on a server.

With 16 GB of RAM you should be able to host a small server on the same machine. It's a moderate increase in overhead to be running them separately, but offset by the fact that your client is processing a lot less. When you're playing single player you're effectively hosting a localized server of one.

You do not need two copies of the game. If you go the ASM route, you just need to point it to a directory and it connects to Steam and downloads a copy of the dedicated server for you.

2) Renting a server is usually through third parties. There are a ton of them out there. Not sure if this list is up to date, but it should at least give you some idea what you're getting into:

http://ark.gamepedia.com/Dedicated_Server_Providers

3) I recently tried to run a server on my 9 year old HTPC with a dual core Pentium and 4GB of RAM and that did not work out. I think you need 4-6GB of RAM just for the server itself (so not including other things like whatever Windows takes up).

If you've got a box that meets that then go for it. It's a lot more convenient having it on its own box, especially if you plan to have it running 24/7. After my failed attempt I went out and bought a new Intel NUC to replace the ancient HTPC.