Portable countertop induction burner questions

I've been researching and really want to get a portable countertop induction burner as our current electric stove isn't cutting it. We've got a fair amount of pans that will work with induction, but I have a few questions.

1. I have cast iron pans from Lodge but these do not have straight flat bottoms. Some have pictures, similar to the wildlife and Dolly Parton series and our largest pan has a raised circle around it diameter (the center of the pan would not touch the surface). Will these pans work because of their limited surface contact?

2. My largest pan's base is 12 inches in diameter, how would that work on what's available on the market?

3. What is a really good portable burner that can accommodate the 12" base (assuming I can use it because of the raised diameter circle I described above in question 1).

Thank you in advance.