This is called a "steeplechase".
No.
It is known as a steeple-chase.
SteepleChase is the race that includes jumping hedges/fences when the horses are running together. Cross-Country is a timed individual run across all kinds of barriers
they are called mustangs. they are the American wild horses. Australian wild horses are called brumbys.
They are called a herd of horses.
Horses, generally.
Horses are just called "horses" unless they are in a group together. When horses get in a group together, they are then called a "herd".
American wild horses are generally called mustangs.
STB is short for Standard bred: bred for harness racing. TB is short for Thoroughbred: bred for racing on the flat or over hurdles.
a herd of horses
A group of horses can either be called a band or a herd.
Adult female horses are called mares. Adult male horses are called geldings (castrated) or stallions (not castrated or uncut).