To be a home office the space has to be used exclusively and regularly for business. If it qualifies then all the mileage you described is business mileage. If not, you would track the miles from the market to the store and back to the market or to another store. But miles from home to the first place and miles from the last place of business to home is commuting and not deductible. Any reasonable way to log those miles would be acceptable.
You are correct about reporting as you described in #4. The only amount that affects your tax liability is the number of business miles.
