A heat exchanger would be more compact than sticking a pump down at the bottom.
You can't suck water up from that far down, you have to have the pump down below pushing it up.
Yes you can. We do it for oil wells even deeper sometimes. Although most geothermal units do operate as a loop, the lift can be done, but the closed loop is more energy efficient.
ESP Systems
http://www.pump-zone.com/pumps/pumps/electric-submersible-pumps-in-the-oil-and-gas-industry.html
About 15 to 20 percent of almost one million wells worldwide are pumped with some form of artificial lift employing electric submersible pumps. In addition, ESP systems are the fastest growing form of artificial lift pumping technology. They are often considered high volume and depth champions among oil field lift systems.
Found in operating environments all over the world, ESPs are very versatile. They can handle a wide range of flow rates from 70-bpd to 64,000-bpd or more and lift requirements from virtually zero to as much as 15,000-ft of lift.