The description given of God walking with Adam in the garden of Eden actually conotates that the literally physically walked together and talked as we might do with another person.
Not just in the general sense of 'walking with God' as we use it today.
you can see this in the description of how God came after the fall and Adam hid from him. God comes in the cool of the day as per the normal routine and Adam knows he is coming so he hides himself rather than going out to meet him.
When I say that they physically walked together I'm not necessarily implying that God her has a physical body, but rather that he was manifest in some physical/spiritual way which was evident to Adam's physical senses.
also, I believe it was God the Son who walked with Adam in the Garden. The teaching I get in scripture is that it has only ever been the Son who has been revealed directly to mankind (as in the case of Moses as well). We are meant to know the Father through the Son, I don't think that has ever changed.