I watch a boy 24 hours at a time and 14 hours at a time....what should I be charging?

Depends on the going rate for where you are and what you've done in the past. You could use minimum wage as a basis. In CA, that's $8/hr for first eight hours, time and a half up to 12 hours, double time for anything over 12.

Are you reporting it? Do you watch him in your home or his? Is this a regular thing? I would say at the bare min, $5 an hour, for your home and as long as there isn't any drama etc,, involved.

$100

For the 14 hours, is he awake or sleeping? Are you awake or sleeping? For 24 hours I would say $125, for 14 hours if you are awake the whole time I would say $100, asleep part of the time I would say $75.