The most common reason is that she may be pregnant. Delayed estrus may also be a result of poor condition (too thin or too fat), she's been sick which has caused her to become sterile, etc.
A cow can come into heat at ANY time of the year and ANY season. There are no specific environmental conditions that have to occur for a cow to come into heat, unlike with other animals like sheep, goats and horses, for example. Cows come into heat every 17 to 24 days, regardless of what environmental conditions that occur.
Yes, in a way.
No, the cow will not go into estrus after she becomes pregnant.
She will, yes.
Yes. A barren cow (one that is open, or not pregnant) is able to come into heat or estrus.
A cow will come into heat every 21 days, regardless of the time of year, they will not (or at lease should not) come into heat when they are pregnant.
No. A cow or heifer in heat will stay with the herd, or rather, the herd will stick with her.
It could be. It could also be that the cow may be just going in or out of heat and the bull already caught her, which is why he's not interested in her. Without any further information such as if you seen her tail was crooked or she was acting funny in the hind end, this is all I can come up with for you as an answer to this question.
A serious infection of an eye disease like pink eye, cancer eye or even cataracts (that come with age) can cause blindness in a cow if not treated, or if caught and treated too late. Sometimes genetics can cause blindness too, or being kicked in the head by another cow.
Only if the cow that they're mounting is in heat.
This really depends on the cow. Often it is the one that is being ridden that is in heat, however the one that is in heat can also ride other cows (and even the bull). The one that is in heat is the one that stands to be mounted and doesn't try to turn around and butt the other cow that had just ridden her.
Estrogen does not cause a lactating cow to be lame. Feed that is high in energy and protein (like grain) can cause a cow to founder (or be lame). Injury is also a likely cause for a cow to become lame; a cut that has invited infection will also cause a cow to become lame. But not estrogen.