I booked an airline ticket for a domestic flight in the US through www.aa.com, and it does not ask for any passport details. Is this normal? Also the site says that it take 3 hours to send ticket confirmation.
Is this normal?
This is all very normal. A passport is not required for a domestic flight in the US, and many Americans do not have passports, but you will need one of the forms of ID accepted by the TSA (a passport is one of them). US airlines do not collect passport information for domestic flights, just full name, date of birth, and gender.
A delay while the booking is ticketed through the airline's IT systems is also typical. In my experience, they usually quote an estimate of a few hours, but it often takes just a few minutes.