basically, given your situation, you are due pay from arriving at the shop (considering that as the actual starting time) and when you leave the shop at the end of the day (presuming you leave at your quitting time).
You are not owed travel time to or from home.
Your employer can pay you a reduced rate for the travel time as long as it meets or exceeds any applicable minimum wage.
Because that is "earned" pay, it is taxable. If they are not withholding taxes and whatever from that pay, they are in violation of the law.
this is all with the presumption you are not covered by a collective bargaining agreement or some other exception to the law based on a specific job description.

