I agree with SilverFeral, what I see is bowel inflammation which could be caused by a pathogen or food.Is this a racing bird? This type of excess urine can be caused in the morning prior to feeding, of if a bird is nervous and disturbed by something, that sounds like it as you say pigeon is more active than normal. But at the same time "rice water" poops can be a sign of a inflammation in the bowel caused by a pathogen. So it is best to take the poop to be checked at the vet. Unhygienic conditions will not cause this poop as if bird is stress by filth, but unhygienic conditions will cause disease so always try to keep the place clean. If that is cardboard and it is not swapped for fresh sheets regularly it can easily mold, or even help bacteria develop on it.