#2 - Bulls can be cut or banded at birth. The longer after that the harder it is on the calf. Probably the majority of breeders castrate <2 mos.
You're 1 & 3 questions are a little mixed up.
COWS get bred "back" after having their calf - usually it will take 30-45 days before they have a first cycle. Many people have a "calving season" - anywhere from 45 days to 3 months? So, most cows will be about 60 days post calving when they get re-bred.
HEIFERS (a female that has not had a calf) get bred for the first time. Depends on your management system. Some producers wait til they are 2 years old to calve at 3 yrs old. But, most of the industry breeds heifers at about 15 months of age to calve at 2 years old. In order to do this successfully, they need to be grown out properly. They should be about 65% of their mature size. So, if your breed has a mature weight of 1200#, a heifer should weigh about 780# at the time of conception - and should have great nutrition provided thru calving. (great nutrition can be, & usually is, just good pasture & good hay in the winter).