How invasive is the procedure for veneers?

Cosmetic veneers. The amount of tooth enamel removed for the placement of veneers depends on a number of factors: whether your teeth are straight or crowded, the size, shape and color of your teeth, your bite, whether you have any parafunctional habits (bruxing). Another determining factor is the desired outcome of treatment. Some veneers can be placed with minimal reduction, while others require more.
Prep vs No Prep. No prep (not invasive) is the most desirable because no shots are needed and no tooth structure is removed. Another options are The other two techniques are minimal prep and traditional prep techniques. Your cosmetic dentist can help you decide which procedure is right for your individual case.
It depends. With veneers the amount of teeth removed depends on the position of the existing teeth and the desired outcome. In some circumstances on can do a no-prep veneers without anesthetics or reduction of the teeth.
Depends. You will hear of prepless veneers or veneers without drilling. I have been doing veneers for 25 years and have yet to do them without removing tooth structure. People do "prepless" veneers. Usually they are bulkier. The difference is in the color/condition of the teeth and the desired result. The whiter you want and the darker the tooth, the more reduction needed to mask the color.
Depends. There are two types of veneer proceedures that are done today. The first is the traditional prep veneer where we reduce the face side and biting edge between 0.5mm and 1.5mm for the porcelain veneer. The second is what is termed no-prep to minimal prep where no tooth to minimal tooth structure is removed. Not every case can be done the second way. Your dentist would have to make that determination.
Consult your dentist. I recommend that you consult your dentist about the expectations of you specific procedure. Wishing you the best.