What did squires do in the middle of a medieval battle?

As known to most of the people above me, training from the Page(7-14 years old) started off light in only preparation whereas the Page would run errands and do busy work for the Knight.

I do not agree with the statement above that there were 30 year old Squires seeing as how the knights were constantly in battle which almost guaranteed the constant need of new knights to fill the old one's place.

But during this time period the squires almost had it easy, not very well known or even thought of today but fighting back then was very different from today, people had a lot of chivalry in battle, they would not target squires or kill them, in some fights, the fighting times would be respected and they would even ceasefire at night.

Although it must have been tough for the squires because they had to carry all of the knights stuff and bury him, and even dress him for battle, they still always had the option to grow up, they would have next to no chance of dying from a strike on knights.

You might be asking how this addresses the question, They were mostly there for experience, everything you listed seems to be true, but their main focus was to gain experience and learn about battle and what they were required to do, stabbing at a dummy for 7 years won't prepare you for an actual battle, so they were there to help out the knight no doubt, but they were also there to learn and gain experience.

There were many career squires, who were virtually synonymous with men at arms. Becoming a knight was expensive and came with obligations that the younger sons of knights could not always manage. Also, even those who became knights often weren’t knighted until well after age 21 and had fought in many battles before achieving knighthood.

This is utter nonsense: "When his horse was felled, the knight, weighed down by by his armor and tangled in weapons, shield, and spurs, was likely to be captured before he could manage to rise."

The author of that was repeating rather silly myths. Full body armor did not weigh more than 65 to 70 pounds, about the same weight as most modern soldiers carry and it was distributed throughout the body. The knight had no problem getting up when a horse was killed. There are plenty of videos on Youtube demonstrating how easily one can move, get up, climb, etc in full armor. Here is one: https://www.youtube.com/watch?v=qzTwBQniLSc

Moreover, knights frequently fought on foot. The list of weapons they supposedly dragged into battle is a bit absurd. No, they normally took a lance, sword or battleax and dagger.

As for what squires did in battle, their job was aiding the knight in whatever way the knight needed. It varied considerably.

I always thought the squire rode beside his knight to assist him. In the Battle of Lutzen in the 30 year's war (post medieval) King Gustav Adolphus of Sweden gradually became separated from his headquarters group until only his 18 year old German squire was with him and was mortally wounded when the king was killed.

Barbara Tuchman provides a a partial answer in A Distant Mirror: The Calamitous 14th Century:

At fourteen or fifteen, when [the young noble] became a squire, the training for combat intensified. He learned to pierce the swinging dummy of the quintain with a lance, wield the sword and a variety of other murderous weapons, and know the rules of heraldry and jousting. As squire he led his lord's war-horse to battle and held it when the fighting was on foot ...

Because of the necessity of donning armor with all its straps and buckles, battle was a more or less fixed engagement, arranged by the logic of approaching positions. The invention of plate armor early in the 14th century now supplemented chain mail, which as penetrable by the crossbow ...

[The knight] began battle with the lance used for unhorsing the enemy, while from his belt hung a two-handed sword at one side and a eighteen-inch dagger on the other. He also had available, either attached to his saddle or carried by his squire, a longer sword for thrusting like a lance, a battle-ax fitted with a spike behind the curved blade, and a club-headed mace with sharpened, ridged edges, a weapon favored by martial bishops and abbots on the theory that it did not come under the rule forbidding clerics "to smite with the edge of the sword."

The war-horse carrying this burden was itself armored by plates protecting nose, chest, and rump and caparisoned with draperies that got in the way of its legs. When his horse was felled, the knight, weighed down by by his armor and tangled in weapons, shield, and spurs, was likely to be captured before he could manage to rise.

I get the impression that squires would have remained at the periphery of the core battle zone, helping their knights in preparations as they mounted their horses or drew new weapons. Battles would have begun as highly stylized affairs, but as these things go: once one side gained a decisive advantage, all gloves would have been off and squires and other bystanders would have had to "improvise" and struggle for survival.

Tuchman includes accounts where the strength of a lord's force is head-counted in knights, squires, other men-at-arms, archers, and foot soldiers, which may indicate that squires (along with their knights an other force elements) became involved in battle fairly regularly and perhaps (also) at early stages.

That's not exactly how it worked. As not everybody was able to become a knight (especially without richness), many squires were adult, sometimes more than 30 years old, and because of their experience, they were well-trained fighters. Don't think of heavy cavalry only as knights.

For example, the regular heavy cavalry unit in Poland was called Chorągiew (that's the name for a very big flag), in 15th century counting around 500 riders. But not all of them were knights. Each knight was leading so called Poczet, which counted not only at least one squire under his command, but also other "fighting servants", who were providing support, guarding backs of the knights. More important knights could have Poczet counting even 30 horses.

The painting Battle of Grunwald by Jan Matejko, which you can see in Warsaw's National Museum, depicts the Battle of Grunwald, one of the biggest in medieval times, between Kingdom of Poland and Grand Duchy of Lithuania vs Teutonic Order in 1410. On the left side you can see Casimir V, Duke of Pomerania on his horse, fighting with Polish knight Jakub Skarbek and his squire (below, hanging on prince's horse).