Would I need a car if I lived in Yanchep?

Yes or no to "needing" a car is very subjective.
A car would be helpful if you have to go to different places with the kids (think sports events etc)
Otherwise, you could get away without a car as there is a bus connection to other suburbs and the train station in Butler, which is end of line (at the time of writing, July 2021). The Yanchep rail extension and train station is due to open next year which will make life even easier and could eliminate the need of a car.
Depending on your place of residence you can walk to the shopping center, medical center, beach etc.
I hope that might help?

You could also cycle hah. Depends where you are in Yanchep. The Yanchep Central shops are now open so shopping for your everyday needs just got easier. Commuting to the city can still be a pain (50 mins drive) but park-and-ride from Clarkson to save yourself the hassle if you're working in the city. In summary, I'd get a runner car to get around the suburb and around.

Yes, pretty much! It is too far away from anywhere else to walk places - except the beach and the local stores if you are not too far away. If you needed medical treatment, had kids in school or pets needing vets in a hurry you would really be stuck. Major shopping is a fair distance, so you would need to travel quite a bit to get everything you need.