No. The best way to tell a cow is pregnant by rectal palpation or blood test. Deciphering whether she's pregnant by her udder is much different than seeing if she's about to give birth. An udder will often get enlarged and the teats will look full (as well as the vulva gets looking loose and floppy and the area around her tail head looks looser too) when she's close to giving birth.
Talk to your cow. If she is pregnant your character will mention how see and her baby is doing. If your character does not mention a baby then your cow is not pregnant.
A heavily pregnant cow, or a long-bred cow. Or, a cow that is expecting soon.
A pregnant cow who gives birth is a mother.
No, the cow will not go into estrus after she becomes pregnant.
Bred cow.
human sperm cannot get a cow pregnant. The only species humans can get pregnant with their sperm is another human.
An open or barren cow.
No.
No.
A springer or springing cow.
A Springer cow refers to a pregnant cow expected to give birth soon or has recently calved. They are typically in the late stages of pregnancy or have just given birth. A regular cow is just a general term for a cow that is not specifically pregnant or in the immediate post-calving period.
Until her udder and vulva start to swell late in her third trimester, the only way to tell a cow is pregnant by looking at her is that she's getting pretty round in the sides. You can also bump her side gentely with your fist and feel the calf inside her. The best way to find out is to have your vet do a pregnancy check on her. To determine if a dairy cow is pregnant, feel the area immediately to the SIDE (left or right) of the base of the tail. If it is hard, the heifer or cow is not pregnant, if it is soft, she is pregnant. I recall this from many many years ago when I was a teenager working on my uncle's dairy farm. Another way is to see if the cow comes in to heat again (21 day cycles). This is demonstrated by bulling behavior. A cow in heat will stand and allow another cow to mount her or attempt to mount another cow. If the cow being mounted walks away from the attempt, then in all probability the cow that was on top is in estrus. See the related question below for more info.