My application requires a DC geared motor with torque of 10 NM - 20 NM and low speed (25 RPM at most) and a small dimensions (120 mm length at most). I failed to find my specs at eBay, and Alibaba targets only mass production. Can you recommend me certain models of Gear, Stepper or even Servo motors that met the above specs from any online store?
You can find DC gearmotors on Amazon with roughly those specs.
This one, set with 30rpm and 24v, is fairly close: https://www.amazon.com/uxcell-Torque-Electric-Reduce-Turbine/dp/B072DTMPBC/ref=sr_1_5?s=hi&ie=UTF8&qid=1511799633&sr=1-5&keywords=dc%2Bgear%2Bmotor%2B25rpm&th=1
This one has higher RPM, but more power, and you can add an extra 2:1 gear reduction: https://www.amazon.com/dp/B01N8YDOC9/ref=sspa_dk_detail_2?psc=1
That's the smallest you'll find in fairly cheap motors. Otherwise, you'd need to custom order one, or talk with a manufacturer/supplier, which will probably be more expensive.
Ex: The AST 9AFG is less than 50mm long and has a version can deliver over 10NM at 21RPM. They have larger ones too