yes they had the height advantage over opponents walking on the ground
Horses did not live whith Knights.
they fighted on horses
tall and strong ones like quarter horses. Depends on the knights.
knights rode horses like any other person would ride a horse
One of the original limiting factors on the amount of armor a knight could wear was the weight his mount could carry. As warmbloods (draft horses crossed with Arabian-descent horses) were developed, knights got larger horses that could carry more weight and still be useful in battle, allowing for the knight to wear more armor.
Horses
Friesian horses were popular war horses, and mounts of knights. For the Howrse game for Archimedes the answer is "for carrying knights".
The squire. The squire would carry the knights weapons or armor, hold any prisoner the knight might take, protecting the knight, and take care of the knights horses.
Horses were important to knights. In fact special heavy horses were bred for them.
Seeing as to how each side starts with two knights (horses) there are four knights at the start of the game. If a pawn is promoted to a knight there can be more than four knights on the board, but this doesn't usually happen.
Probably their steed. I doubt they'd use the horses real name.
Carried knights into battle and trampled people.