Yes, modern chainrings have teeth that vary from each other. They are formed that way to enhance shifting between the different chainrings. Older chainrings from a couple of decades ago had teeth that were symmetrical as they did not have the advanced profiles in use today.
The creaking you were experiencing was probably due to either one of the chainrings being loose or your bottom bracket being loose or worn out. The bottom bracket is the bearing assembly at the bottom of the bike frame, where the seat tube, the down tube, and the chainstays intersect. It is possible that an extremely worn chainring could also cause noise, especially with a fresh chain (a new chain on an extremely worn chainring can creak in its "displeasure" with not being able to smoothly engage with the chainring).
The likely cause of the creaking you are hearing is either:
- A loose bottom bracket in the bottom bracket shell
- A loose crankarm on the bottom bracket axle
- A worn out bottom bracket (not as common)
- A loose chainring
- Worn chainring(s)
In the interest of ensuring that terminology is clearly communicated to the questioner, I am adding some images.
First, this is called a crankset. It includes the chainrings (what engages with the chain), and the crankarms (the arms that the pedals screw into). In some cases, the crankset includes the axle connecting the right and left crankarms, but not in the case of the model identified in the question.
Next, this is what your bottom bracket looks like. This model includes the axle, and each end of the axle has a tapered square shape that the two crankarms engage. There are other engagements besides the tapered square, and also bottom brackets that do not include an axle (for cranksets that include the axle).
Finally, this is what is called the bottom bracket shell. It is part of the bike frame and is where the bottom bracket is either screwed or pressed into when the bottom bracket is installed.