Stats are tallied every day and will be reflected on your league standings the following morning.
The IP max is adjusted every day is a season long max for all your pitchers combined. You total IP to date will be updated every day as well, so you always know how many you have left. If you don't use up all the innings available to you nothing happens, so what most guys do is try to ride a little bit ahead of the pace over the first 2/3s of the season because you'll often see guys on innings limits and whatnot who won't pitch as much later in the season. Plus there's injuries ect ect. Anyway, yahoo (or ESPN or whatever) will track this stuff for you.
Good luck in your first fantasy season.