Does anyone know how long we will have to do the New Year's Quests? Tonight only? A week? Will the quests reset everyday?

no, we don't know. but most new year's celebrations in the past have been for a week or less.

No, the quests probably won't reset every day. I think they just did that because the bags weren't released at midnight last night and so it would have been unfair to those who already did their quests to not reset them and everyone else would have had an extra day to collect tokens.