rough Idle and engin noise

Is it a squealing noise when you start it up? That could be a loose or worn alternator belt. More info for you: Your car has a timing belt rather than a chain. It could also be that that the water pump or the t-belt tensioner bearing could be failing and that could make plenty of noise. Here is a directory and estimator link for you: https://repairpal.com/mazda-repair-in-north-miami-beach-florida https://repairpal.com/estimator/mazda/millenia