'Make a walk' is wrong. 'Do a walk' might be possible in some highly specific circumstances. It is not possible to say it in a general sense to mean 'to go for a walk.' However, if someone adopts a manner of walking which is different from the way they normally walk, you might say that they are 'doing a funny walk.' And if someone is doing a sponsored walk for charity for example, you might say they are 'doing a walk for charity.' As you can see these are quite specialised situations.

Neither, in most cases. The usual expressions are these: take a walk (US) go for a walk (GB).

I am going to take a walk.

Neither, but you can take a walk.

Unfortunately you can't say neither of them. The correct form is just "go for a walk" thus when someone is asking what you are doing you can answer "I went for a walk". As you are not creating the walk you are not "doing" or "making" it. Just like even though "I'm doing a marathon" may sound good, the correct form is "I'm running a marathon"