Is it the norm for banks to allow a minor (age 17) to open either or both types of accounts in America?
It is not the norm for banks to allow minors in the United States, under 18 years of age, to open a checking or savings account. It is however the norm for banks to allow accounts to be opened by custodial account holders on the behalf of a minor of any age, even less than 1 year old.
My bank (Wells Fargo in the US) says that accounts are available to teens ages 13-17 with an adult co-owner. As a teen my first bank account (at a different bank) was also co-owned with my dad, so this is normal for me.