Wouldn't "Are you coming on foot" also be right, according to the non-distinction of "going/coming" as presented in the lesson?
In Czech that would be "Přijdeš pěšky?"
Which non-distinction do you have in mind? They are not always interchangeable.
What is wrong with "Do you walk?"
It must be "Are you walking?". That means right now. Do you walk is "Chodíš?"
Well, that sounds reasonable. I'll try "Are you walking" next time :-).