There is a problem with "the new game" option in game, when you have loaded a save before and use the "exit/start new game" ingame option. Then you have not a new game, you have only a new intro sequence and continue on the loaded game states before. If you want to start a real new game, you need to hardreset the game-engine (close and restart the game). Using the softrestart leads to uncontrolled behavior. I think all your reported bugs could be such uncontrolled behavior.
1 is cheating ;-), if you do such things, game engine knocks back. :-P
2 and 3 could be uncontrolled behavior of softrestart