I do not know if I should miss one quest. Maybe the reward system may get resets if I miss one
Missing a day does nothing to the angler quest or rewards. You're fine. The only thing the rewards depend on is the number of times you do them. Short and sweet.
See this page for more details. I'd recommend reading as much as you want on the Wikipedia for Terraria. It's very robust, and has a LOT of information about the game, most of which isn't something most of us wouldn't pick up on otherwise (I know I sure didn't!).