原文Madame Masque doesn't need to have been under your control when the first card is drawn for her last ability to trigger. As long as you control her when you draw your second card in a turn, that ability will trigger.
原文Once an ability that causes a creature to connive begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the conniving creature after you discard a nonland card but before it receives a +1/+1 counter.
原文If no card is discarded, most likely because that player's hand is empty and an effect says they can't draw cards, the conniving creature does not receive a +1/+1 counter.
原文If a resolving spell or ability instructs a specific creature to connive but that creature has left the battlefield, the creature still connives. If you discard a nonland card this way, you won't put a +1/+1 counter on anything. Abilities that trigger "whenever a creature you control connives" will trigger.