Yes, the space used in your home to store and repair items for resale can be considered a home office. It must be used regularly and exclusively as your principal place of business.
These terms has some specific definitions as related to the home office. The following articles will give you more information and examples to be sure that your situation does qualify:
Can I take the home office deduction?
What qualifies as "principal place of business" for the home office deduction?
As for the mileage, each situation you described would be considered business miles. Be sure to keep a log documenting the business miles driven as well as a record of the total miles driven for the year. Both of these numbers will be needed in your return whether claiming the standard mileage rate or actual expenses.
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