Hi Evelyn. In addition to the answer you’ve already received, I think that you should probably make sure that you can legally have the studio in your home under your local zoning laws. The worse thing would be to do everything to prepare for your studio (e.g. equipment, insurance etc.) and then find out that the zoning laws do not allow for your business.
You are correct in being concerned not only for your own personal professional liability, but also that of your studio, AND I might add of your home. Talk to your insurance agents to make sure that you are covered ALL around and that you don’t run afoul of your home ownership or home owner’s insurance policy.
My two cents.