Is there a grocery store close by (walking distance)? Or any tips on getting snacks, breakfast items, milk etc?

There isn't a grocery store nearby

You can get it all at the stores and restaurants near the hotel lobby. I don't remember any store close enough to walk.

Yes their is a Wal-Mart on Kirk man road or on doctor Phillips

None within walking distance, but the Bayliner Diner inside Cabana Bay will have many of the items you mentioned