Would they be comfortable for someone that suffers from planter fascitis?

Absolutely! I had Plantar Fasciitis in both feet. Spent $$$ on orthopedic shoes and all kinds of apparatis hoping to relieve the pain. The Croc Kadee flats were thr only shoes I could find that relieved the pain. I highly recommend them for anyone that suffers from plantar fasciitis.

How do choose a size? It's just add to cart, I can not find any information in the description nor the chart someone mentions in the Q&A.

There's something wrong with this listing. There IS NO size list to choose from. There is a size CHART to help you decide which size would fit you, but there is no dropdown menu anywhere to choose which one to order. Oh, well. Price too good to be true. The next cheapest option I found for this Crocs Kadee is $24.99

I was thinking of purchasing these as a gift for my friend who has a narrow foot, how wide do these run?

They run about average width, but they definitely have some give to them. I normally wear wide width and these were very comfortable for me, so you might think about getting her some footie socks along with it.