I have overlays on my nails so I don't know if they are stronger or not, they are certainly growing faster than they did, and my hair's grown loads too.
I haven't been on the diet long enough to notice yet, but this happened to me when I went on a juice fast for nearly a month. Must be something to do with not eating 'food', lol! (Seriously tho', I would love to know the answer.) I'd love it if my hair grew, it's never grown beyond shoulder length ever in my life (neither did my mum's - even the hairdressers can't explain it).