What does “non-character” mean in Buzz’s Secret Mission ability?
It means any card that isn’t a character card type, so the effect will trigger only if you pay 2 {I} or less to play an action, item, or location.
Official set release notes — Wilds Unknown
Does Buzz’s World’s Greatest Toy ability trigger if I use a payment modifier to play a higher-cost card for 2 {I} or less?
Yes. That ability only cares about the total ink cost paid to play a card, which is determined after all payment modifiers are applied. As long as you paid no more than 2 {I} to play a card, the World’s Greatest Toy ability triggers. The same holds true for his Secret Mission ability. For example, if you played a cost 3 card and modified the payment to pay 1 {I} less, you paid a total ink cost of 2 {I} and the ability triggers. The Family Scattered The Family Scattered
Official set release notes — Wilds Unknown