You do not need a bank account to get a job. You need it if you want direct deposit. You MUST have a parent or guardian sign you up for an account if you're under 18. You cannot have your friends mom sign for you.
At least in the U.S. a minor under 18 is required to have a parent (or legal guardian) open a supervised account for the kid.
Get an account with your mum. Don't get an account with your friend's mum - she will then have access to your money, which is probably not a good thing.
no