These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
If there are already more monsters on your opponent's side of the field when you activate "Kaiser Colosseum", nothing happens to your opponent's monsters but your opponent cannot Summon any more. Also, if the number of monsters controlled by "Kaiser Colosseum"'s controller is reduced, the opponent does not have to remove any of his monsters.
If all monsters of "Kaiser Colosseum"'s controller are destroyed, "Kaiser Colosseum"'s effect no longer functions until that player has at least 1 monster again (when the effect re-activates).
If the player who controls "Kaiser Colosseum" has his only monster taken by the opponent with "Change of Heart", then the opponent can place more monsters because "Kaiser Colosseum"'s effect is no longer active until the player has at least 1 monster again.
When "Kaiser Colosseum" is active, and "Cyber Jar" is activated, if your opponent would control more monsters than you, your opponent has to destroy monsters equal to the difference; the excess monsters are never actually Summoned and instead are sent from the Deck to the Graveyard (so "Witch of the Black Forest" does not get its effect, etc.). So the monsters are destroyed after they are picked up, but before any monsters are Special Summoned for the effect of "Cyber Jar".
While you have "Kaiser Colosseum" on the field, your opponent can Tribute Summon, if after the Summon they will control less or an equal number of monsters as you do.