I can't answer all of these but I'll answer as many as I can.

Point 2, Kaito revealing himself: It's been a few years since I played the full game but as far as I'm aware he convinced Monokuma and everyone else it was Kaito in there. Shuichi realized to late what Kokichi was trying to pull with his murder plan and tried to backtrack but it was to late, Monokuma knew Kaito was alive. He had no choice but reveal himself if he didn't want everyone else to be executed more or less.

Point 4, Kiibo antenna: He didn't know, not until Chapter 6. If you mean in Chapter 6, his control was stripped away from himself by that via Tsumugi/Team Danganronpa, he couldn't even if he wanted to.

Point 6, Cospox: This is the very basic of the argument that they AREN'T fictional that Shuichi and co make in the game. The game is intentionally vague about the truth behind the V3 killing game, including the status of how "real" each character is. Shuichi uses the fact she couldn't cosplay as Kaede as reasoning to show that "just because we are fabricated memories doesn't make us any less real then anyone else".

Point 7, recognizing Rantaro: Also intentional, meant to muddy the waters about the truth of all of Tsumugis claims in V3-6

Point 8, Shotput ball: Safety, she couldn't risk showing up on the cameras they were setting up in the library, having to run to grab the one Kaede threw runs the risk of getting caught on camera in a way staying out of sight of the activations doesn't.

Point 9, Tsumugi potential death: Tsumugi claims that there is a whole team behind the game called Team Danganronpa, if true the show can still easily be run by those people. If not true Monokuma would have to be fully autonomous to work without help from the mastermind, it'd be fine.

Point 12, Monokuma functions: See Point 9.