Yes. Just like any other invasive procedure - if the guy pricking your skin has something - you have a chance of getting it -.
Yes. Because hepatitis b is a bloodborn virus, any activity that risks contact with other people's blood is a risk. Traditionally tattoo parlors and those who do tattoos without proper training have been a concern. Awareness of proper sterilization techniques has increased, so using a reputable, certified tattoo shop conveys less risk than previously.
Yes. You are only at risk is universal infection precautions are not carried out. Ie. Sterilization, disposable needles, etc. Homemade or prison tattoos where the sharing of needles or ink is common is a common source of hepatitis b transmission. Be sure to ensure that your tattoo parlor uses proper sanitary precautions and techniques.