[mod]

For what it's worth, tinder is easy to come by in most environments. Also in those days, you would likely try to never make another fire, and instead keep yours going.

Somewhat true today as well, as firelighting tools are all consumables. Some may light thousands of fires, but still would fail to eventually.

[xxs]

All you need is a lens given a bright day. I used to ignite paper as a kid. It should be possible to use ice as well but it has to be properly shaped and the water to be clear.

[iamthirsty]

Doesn't really seem like ice would be abundant on a desert island.