I've heard about Mechanical-hydraulic hybrid brakes but didn't find any examples.
Are they exist? If yes, are they comparable with hydraulic?
Looks like the TRP Parabox Hydraulic Disc Brake is what you're referring to. Basically it allows you to use your existing mechanical brake levers to control the hydraulic pistons. So you can use your old brifters, and still have hydraulic braking. Here's a review that explains how they work, as well as provide and idea of the performance characteristics.
Avid makes a series of mechanically-actuated calipers. These are paired with a Disc to provide a brake.
Their performance is comparable. Many people prefer Hydraulic though, as the fluid tends not to compress, which yields a more precise "feel" than a cable-actuated mechanism. One up side of the mechanical calipers is their reduced maintenance requirements.
No, these don't exist. You can get cable-pulled disk brakes and hydraulic disk brakes. Also you get cable-pulled rim-brakes or hydraulic rim brakes Sram S-700 (thanks to @mikes for the pointer) or Magura variation:
Unless by "hybrid" you mean something different. I understand that you are asking if brakes exist where both fluid and cable are used in propelling pads to rim or rotor.
UPD: If such thing exist, please let me know, I'll be very interested!
UPD 2: I stand corrected. Turns out these exist. See Kibbee's answer.