You need to use an element that fits the size of the bottom of the pan, not the top -- this happened to me yesterday with a parabola-shaped Dutch Oven. I first put in on an element that seemed to fit the size of the pot, but it was really too large because I was eyeballing the top of the pot, and the element turned itself off as it didn't sense a pot on the element. When I moved it to a smaller element, it worked fine.

Toronto Veterinarian is right that it's the diameter of the pan's bottom that counts. If GE Profile's induction is like my brand (and it probably is), there's leeway with pan sizes. You can use a larger or smaller pan on the burners, just not to the extreme. I think mine work with pans that are a half inch to an inch beyond the circle that marks the burner diameter. Tonight I cooked dinner in an 8 inch diameter pan on my 11 inch hob. By the time I realized my error, dinner was almost done. Nbd. Also, pans don't have to be perfectly flat -- I have some old cast iron with a slight wobble, & they work great.

Re hum, from what I've read on the internet, it's mostly from clad or sandwich bottom pans. Depends on the quality. My cast iron is silent. A Tramontina tri ply stock pot makes a tiny tsssk sound, my Kirkland sandwich disc pots are a bit louder. All are quiet enough that as soon as food starts to sizzle or boil, the pan noise is drowned out.

My experience has been that my heavier, higher-quality pans (cast iron, my monster 12 in demeyere skillet) are less buzzy/more quiet than the lighter, generally less expensive ones (the Calphalons and my cheapy one from Target "sing" at times). I can't speak to all cooktops of course but I think that pan quality has more bearing on those issues. That said, the buzzy pans still do get hot and cook food!

Using two pans close to each other can also cause a kind of interaction and a high pitched sound.

Yes, using pans very close to burner size works better -- both for performance and for noises. Rather than buying a box set of pans it would be worth it to look at the actual sizes of burners you have and buying pans that match them well and have wide flat bottoms.

Frying pan: for $20 you can try this 10.25 inch Lodge two handled skillet. If you learn the concept of seasoning, it will be fairly non stick (not perfectly, but mostly). Looks like a useful size, manageable at 5 pounds, & goes in the oven too.

https://www.amazon.com/Lodge-L8SKL-Cast-10-25-Black/dp/B071VT8PL8/ref=asc_df_B071VT8PL8/?tag=hyprod-20&linkCode=df0&hvadid=198091976077&hvpos=&hvnetw=g&hvrand=14608571496053990691&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9003445&hvtargid=pla-365809204313&psc=1

Regarding not-flat bottoms: My cast iron frying pans have words stamped on the bottoms and aren't perfectly flat, but they work better if I place a sheet of paper towel between the pan bottom and the element.