A couple people did send some information, that the tattoos shouldn't be a problem. I asked if I would be permitted in the mikveh with tattoos. The response I received was that anything I did to myself before I converted had no effect, and all they could do was ask that I not get more tattoos. So I felt better about this. I was still concerned about my piercings.
Nothing is new, and they are all well-healed.
I have both nipples, daith, tragus, nostril, and a couple of outer ear cartilage pierces. I spoke to my piercer and he said he would be happy to remove and reinsert all the jewelry for me. At the actual mikveh, there was an attendant who came in after I got undressed and was immersed in the water. She makes sure that you have completely immersed yourself. She was not staring at my body, and the water was so incredibly cold that I had my arms crossed over my chest, and could barely say the required blessings because my teeth were chattering.