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.
Your opponent cannot use “Monster Reborn”, “Scapegoat”, etc. while “Kaiser Colosseum” prevents him from placing new monsters. However, your opponent CAN use “Change of Heart”, “Snatch Steal”, etc.
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the opponent with “Change of Heart”, then the opponent can place more monsters because “Kaiser Colosseum”’s effect is no longer active until the player has at least 1 monster again.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”.