When placing tokens on the quest card, if I end up placing more tokens on it than it's level (forgive my lack of correct terminology), will the left over tokens be placed on the next quest card, or no?

Thanks!

No. The new stage of the scenario starts without any progress tokens on it. See p.22 in the rule book (Quest Advancement): "Additional progress tokens earned against the quest do not carry over to the next stage."

Excess progress tokens placed on an active location, however, do carry over to the quest card.

Thank you very much!