Where can I find a hydraulic actuator with these specifications:
12 Volt
Can push about 700 kg
Small in size

What country are you in? Also with that weight why do you need hydraulic? You might find phnumatic to be easier to work with.

Somehow, I think he wants a 12 VDC Linear actuator.

Stroke is also a required parameter.
Feedback method is another. (pulse, resistor)
Limit switches are another. (fixed or adjustable)