1) Most likely there will be some availability on one of the A"A flights throughout the day.
2) You need to call LAN or A"A for that. I believe that in regard to infants, US-Canada is considered like domestic and they don't get charged. I once started a thread on infants on flights and there might be more info there.
3) Yes most definitely but LAN will require you to fax in a copy of your passport to prove that you want to book the ticket for her. And if you guys are flying together they may not even require that.
4) -- Why would you go to Chicago for Sukkos...stay in Yerushalayim! But once you're there, send regards the MLL.