Should it take a week for the car dealer to order a replacement battery for my
2014 Mazda 3 grand touring 4 door car?
Dealers charge too much and don't like to carry much inventory, especially batteries that come in dozens of sizes, and they get stale. Go to an auto parts store and they will even install it free. I have good luck with WalMart batteries, and I like to do my own installation. If the WalMart has a service center, they too will install. And it's a good idea to replace your four year old battery going into Winter. When they get that old, they can fail without much warning and leave you stranded.
Normal for a dealer if it a stock order. I suggest you get a gel cell battery if you’re going to drop big bucks at a dealer for a battery. Gel cells last longer, recharge better have higher amperage output and there’s no corrosion from out gassing.
MOST auto parts stores will NOT install for free. There's no free lunch anymore. Walmart batteries suck.Kirkland batteries (outside the USA) are really good, especially in Canada.
What is also overlooked is the ECU needs preserving or you'll end up with a terrible idle as the ECU needs to re-learn the idle..
@GuruN4KNY Almost all autopart stores do free install. I’m a manager at an Advance Auto and one of the things we do the most daily is free battery and wiper installs.