Can i use OnMouseDown for Mobile games?

Use the GetTouch method: Input.GetTouch

Also if you search the forums and answers you will find examples written for you, example: http://answers.unity3d.com/questions/621539/how-can-i-drag-the-object-with-touch-mobile.html

yes for at least OnMouseButtonDown[0], this will be triggered when a touch begins (cant remember if it will trigger a second time in the event that one finger is already touching when another one begins). I don't think it works for OnMouseButtonDown[1]. Also not sure about OnMouseButton[0] or OnMouseButtonUp[0]

You are better off playing it safe with setting up a separate section for touch though using a system.DeviceType check