1) What do you do for sport?
Does this mean:
a) What do you do to work out?
b) What do you do for fun?
It means neither to me. It means "Which [competitive] sport do you play [on a regular basis]?"
To "work out", you can go to the gym, take an aerobics class, a spin class, walk, jog or many other things that don't class as "sport".
Many years ago, people used to use "to do something for sport" to mean "to do something for fun" but that isn't used in modern-day English, in my experience.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.