1) All thoroughbred racehorses are descended from three 'Oriental', really Arabian, stallions : the Darley Arabian, the Godolphin Arabian and the Byerly Turk, in the C18
2) Stud season. The gestation of a mare is c 340 days. A racehorse is deemed to have been foaled on January 1st of the year in which it is foaled. The aim is, ideally, to have a foal born early in the year. Horses are not fully grown, not fully mature adults, until they are 5. The Classic races (1,000 Guineas, 2,000 Guineas, Derby, Oaks and St Leger) are for three year olds, ( a sort of horse equivalent of teenagers or undeveloped youngsters! ) Breeders try to get the mating done so as to achieve as early a foaling as practicable, within reason, so their 2 year olds (the youngest that can be raced) and 3 year olds are as advanced as possible.
3) A male is a colt and a female a filly until 5 years . Then they are horses and mares respectively. Formerly it was not the practice to put a colt to stud until he was a horse. In recent times the practice has grown up of putting a colt that has won a Classic straight to stud, sometimes not racing him again, sometimes giving him a crack at other top races for 3 year olds and 'retiring' him then. Other colts may be kept racing for further seasons (there are big races for horses and older colts e.g the Prix de L'Arc de Triomphe.. ) Not all great stallions have been great racehorses (and vice versa, in fact few of the latter are really great stallions with big winning progeny !)
4) Yes it is (and the rest!) but the owner is not selling semen just in a tube. The insemination has to be natural.The rules demand it. No artificial insemination is permitted (with good reason: people like to see what they are paying for!)