That clip is very vague in terms of information regarding the physical state of fighters. I have not watched the fight but as per boxing rules, referee are in the position to decide whether the fighter is fit to continue fighting. Maybe he was getting outclassed terribly. The punch he received was a bad one, and referee can always stop a fight in order to avoid further injuries. Boxing is political, so referee can be pre meditated, there has been controversial statements made in that regard.
And yes, the referee should only start counting, after the other boxer is in neutral corner. But that rule is hardly observed in professional boxing, in an attempt to not give extra seconds to the fallen fighter. If you watch closely the ref looks to the panel, where you see a person standing up and counting. In pro boxing the counting starts as soon as the boxer touches any other part of his body other than his feet, and to answer your first question, to my knowledge no. Refereeing and judge decisions in pro boxing is pretty much ultimate and rules does'nt allow boxer to challenge them. In amateur boxing, a judge's scorecard can be reviewed and overturned if a boxer ask for it and the reversal has happened a lot of times in olympics.
