Do I need a power converter or not (I am getting conflucting information)

You are fine. Get a plug adapter

They sell plug adapters in many different stores. Gift stores, bodegas and hardware stores always have them. I have a Euro one and I also have a U.K. adapter.

Your phone and your Mom’s are both fine. I stopped bringing those two voltage hair appliances. Leave it home or buy one in Iceland.
Have a wonderful trip!

Plug adapters are cheap, small, light, easy to find, and probably all you need for everything (except MAYBE for hair appliances). VOLTAGE converters are heavy, and usually completely unnecessary, assuming your electronics are dual voltage and of high quality.

The exception (and the thing to watch for) are any appliances that make heat. A toaster or microwave...look out; MAYBE a hair dryer or curling iron. Depends on the quality of said item. Your iAnything and similar consumer electronics will be perfectly fine. Kitchen or bathroom appliances, things that make a lot of heat, are more iffy. Your curling iron? Hard for me to say (from a guy with not that much hair, limited grooming needs, and zero experience curling anything except his R's when speaking Spanish...).

Ladies...are all curling irons from North America up to the task?

I've used a curling iron without a converter in Europe without any issues, but it was dual voltage. I've also used a dual voltage small hot roller/curler set from Remington several times there without any problems whatsoever.

Thanks everyone!

Mr. E nailed it I think And Sherry, it sounds like what my mom has is similar to what you used and if you were fine, I am guessing she will be too.