Do these verbs like 'walk', 'shop', etc. in these sentences you wrote below refer to one complete action?
Yes, they are thought of as actions that have a beginning and an end. The clearest examples are (1') and (2'). As David told you, you cannot say:
*I'll go walking a mile.
In (2'), the walk has a starting point (the place you are leaving) and an end: your home.
These examples show the difference very clearly, as I see them:
6. I don't know what to do this afternoon. Perhaps I'll go shopping (a long activity with no foreseeable or set end).
7. Today's my friend's birthday. I'll go (and) buy him a present (one complete action).