Use the largest punch that fits, either a 3mm or a 5mm, depending on how big the wart is. I target the biggest or most pronounced-looking wart in a cluster, or whichever one would be the least painful to anesthetize since people generally hate pain. For example, if it's on a toe then those are easy to numb without pain compared to beneath a met-head. In the photos above I might've picked one of the lesions on the plantar left hallux.
After disinfecting the surface with an alcohol wipe I'll drive the punch all the way until it bottoms out at the hilt then cut the base with an #11 blade, flip the plug 180deg using sterile forceps then reinsert. Be ready with some gauze to sponge blood. If it's on a toe then an Esmarch helps prevent bleeding all over the place during the procedure. You might even want to add a small piece of Gelfoam under the bandaid. Cover with a bandaid such that the telfa layer doesn't pull the plug out when the patient changes it in 24-48 hours. Tell them to change the bandaid carefully without pulling out the plug.
You certainly could do two punches, sending one specimen to Path, but I don't do so routinely if it looks very wart-like since it would add a few hundred bucks to the patient's bill probably unnecessarily. If the lesion looks questionable to begin with or if it doesn't respond to treatment pretty soon then I may send a specimen. If it looks like a standard issue wart, has been present for years before seeing me and the patient hasn't died yet, then I reason that it's probably not malignant (fingers crossed) and is just a persistent wart.
I've done it on persistent solitary lesions, yes, although it's not my usual first-line treatment. One patient had a 1cm diameter solitary wart on a lesser digit for years, recalcitrant to several previous treatments before he saw me. Since he'd tried so many other things I went right for the auto inoculation and it resolved in about four weeks.
Edit: I figure that this technique is similar to "needling" as described below but using a punch biopsy instead.
The Treatment of Verrucae Pedis Using Falknor’s Needling Method: A Review of 46 Cases