Is it wrong to use the verb to walk in the progressive form? No, if it fits the context.
I had to choose the correct verb in this exercise.
'Where are you walking/going to?' 'I am walking/going to my office.'
Unnatural. "Where are you going?" "I'm going to my office."
"Where are you?" "I'm walking to my office."
He likes walking/going.
Only "He likes walking" is correct.
He goes/walks a lot.
Only "He walks a lot" is correct.
How often does your son go/walk there for the week-end?
How often does your son go there for the weekend?
How often does your son go walking there at the weekend? (This refers to "walking" as a sporting activity, not simply going from A to B on foot.)