Great Game but could be better

Your first 3 ideas all fall under the fact that each race is designed to give a unique challenge, if every race had all weapons and you could give yourself as much as you wanted then it would remove the challenge.
maybe if when you reached lvl 20 the weapons get upgraded a level above the current max, this would give you an advantage but would still keep the existing challenge of each level.

playing your own music would be good.

the only thing i'd like would be to have cops and racers in free drive. it is there to allow you to practise, so it'd be good to be able to practise. weapons become available once you join a random race or engage police, and as soon as you're arrested, finish race or escape cops the weapons disappear.
no change to your career status, but some side fun and improve your skills with no consequence.