There's nothing you can do to make them grow faster, and as for strength, just nail care like filing trimming, oils, polishes and stuff like that can make them strong. As for length. Nope, they just keep growing non stop. There are people in the guinness book that have disgustingly long finger nails that have gotten all brown and cracked and so long that they curl up into giant rolls of disgusting brown whateverthefuck. ( link ) So no there is no end to how long they get, but there should be a limit set.
Extra calcium might make them a little stronger, and tht would let them grow longer before they break off. They'll only get so long before they naturally break, but some people can get them really long before that happens.
I use a green tea nail polish that is more of an oil that leaves a shine. It keeps my nails looking healthy, and it grows them pretty quickly. Once they start to grow out more I use Christian Dior Vernis Nail Lacquer #001 Natural Clear, which helps make them stay strong and not break (: