Spells that were cast before Ledger Shredder entered the battlefield count. If Ledger Shredder was the first spell you cast this turn, the next spell you cast this turn is your second spell.

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.

Don't play with this card near any important paperwork. We can't take responsibility for what happens.

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.

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.