Can I leave my nipple rings in during surgery adominoplastys & arm lift?

You have the right idea, you can use plastic but not metal. The problem with metal is that the cautery can arc and give you a burn where a piece of metal may serve as a ground and attract the electricity we use to minimize your bleeding.

You will be best off communicating with your plastic surgeon's office directly; the advice you receive online may not be exactly what your plastic surgeon will recommend. In other words, best to follow your plastic surgeon's preoperative/postoperative instructions specifically. Best wishes with your upcoming surgery.

The electrocautery that is used during these procedures sends current through the tip of the tool to the grounding pad, which is the path of least resistance.  If you have metal piercings and for some reason the current goes through them instead of to the grounding pad, you will get horrible burns at the piercing sites that will not be apparent to the surgeon until the drapes are removed.  All metal piercings should be removed. Plastic piercings do not pose this hazard and can be left in place, depending on how high the surgeon is going to prep your skin.  This question must be asked of the surgeon.