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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 “when [that creature] connives” will trigger.

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 counter.

If multiple creatures are instructed to connive simultaneously, they connive one at a time in the order of their controller's choice.

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.

You choose which creatures to phase out after all of those creatures have connived.