I don't know much.......
....but I'd offer:
1) Advantages:
Thrust acts closer to the aircraft centre line, thus reduced yaw in the case of assymetric thrust/engine failure, therefore smaller rudder/fin assembly required, therefore less weight.
Structurally simpler as the engines are effectively bolted on to the relatively solid fuselage instead of dangling from a flexible wing.
Shorter landing gear as no engine ground clearance required, saves space in the wing box and overall weight.
Disadvantages:
Aircraft is effectively restricted to a T-tail design which can be subject to deep stalls.
Noisy in the cabin between the engines (although for a given engine it'll generally be quieter in the cabin than with wing mounted engines)
Limited service access to rear of the aircraft - fiddly to get catering trucks to a reasonble size door.
2) Air under the wing is at higher than ambient pressure, air above the wing is at lower than ambient pressure. HP air escapes round the tip of the wing towards the upper LP area, reducing lift towards the wing tip and creating vortices (=drag). Winglets smooth the interaction of the airflows around the tip of the wing, reducing vortices (less drag) and eliminating disruption of the lift towards the end of the wing (effectively creates a longer, more efficient wing without increasing the actual wing span much). They also look quite futuristic and can be used to tart up an old aircraft design (MD11) even if their actual aerodynamic benefit is marginal in that particular instance.