Why is the AWACS' rotodome located at the back and over the aircraft?
It's mounted dorsally in large part because it's simply too large to fit beneath the fuselage. 

The rotodome has to be that large because inside is actually a planar array. The radar itself isn't round, nor aerodynamic, so it's wrapped in a smooth fairing that presents the same profile regardless of which direction the array is facing.


Caption: The Northrop Grumman AN/APY-1/2 AWACS multi-mode radar inside the E-3D rotodome. (Credit: Scott Carson. Twitter.)

Some airborne radars do not rotate and can indeed be mounted below the fuselage, like the E-8 JSTARS' APY-7 (primarily a ground surveillance radar): 

(Credit: USAF. Link.)

Pave Mover, an APY-7 prototype:

(Credit: Daderot. Link.)

The cancelled E-10 (planned E-3 Sentry and E-8 JSTARS successor) also had a similar under-nose longitudinal array.

(Credit: Defense Industry Daily. Link.)

However, most larger, non-rotating arrays are mounted dorsally and longitudinally, like the Boeing 737 AEW&amp;C:

(Credit: Seattle Aviator. Link.)


  [Question:] Moreover, it seems logical to put the rotodome under the aircraft. Its
  mission is to observe airspace under the aircraft to detect hostiles
  flying low enough to avoid detection by ground radar. 


Not exclusively. Low-altitude penetrators aren't the only targets. AWACS is also tasked with finding medium to high altitude aircraft, both watching for enemies (eg firing "AWCAS killers") and keeping track of friendlies.


  [Question:] By mounting the
  rotodome above the fuselage, the aircraft's wings may disturb the
  radar mounted above them.


You don't need a lot of depression to observe things at medium to long range. At 30,000 ft, the horizon sits just a few degree below level, and even at 30 miles (which is very close) a low-altitude target is just -10 degrees. There's also a fair bit of clearance between the elevated dome and the fuselage/wings, which reduces how much of the ground is masked (roughly -20 degrees from radar to wingtip). Together, there's probably fairly little that an E-3 wouldn't be able to see. You'd have to be practically underneath it at close range. And then you'd have to deal with the fighter escorts...