The first sentence:
I will wait for you until you finish.
سأنتظرك حتى تنتهي.
So, 'until' in Arabic can stand as 'حتى' followed by a limited time, specifically, with waiting.
The second:
We should hand in by 3 pm tomorrow.
يجب أن نسلم العمل غدًا بحلول / في تمام / بموعد أقصاه الساعة الثالثة.
So, 'by' in Arabic can stand as 'بحلول' , 'في تمام' or ' بموعد أقصاه' all followed by a deadline ,specifically, with work deadlines.