The first way would be to enter the cows in, once the cows have been entered in you can then reocord a birth to that cow. This way the program automatically updates the parity, and will place them in order of birth date. The second way would be to enter each calf in just the same way that you have entered the cows in. Entering in a birth date and also assign the dam and sire to that calf. The parity would need to be manually updated in this process. So if that cow had 3 calves you would need to enter 3 in as the number for the parity.
The Animal ID is how you will tell what animal is which animal within the program. The Calving ID is used to identify a birth record, and not the animal that was born. The animal that was born will need to be assigned an Animal ID.