John Reynolds played a role in this too. Buford’s cavalry was the true vanguard, though Reynolds was in command of the advance corps (Meade’s various corps were all strung out at this point and not unified in preparation for a battle). His orders were explicit not to bring on a general engagement, which made sense given the state of his army. Meade also wanted to fight back at Pipe Creek, some 20 miles southeast, and had issued orders to ultimately draw his army together there. To fight in Gettysburg would mean issuing all new orders to generals who were many miles in many directions. There was uncertainty of where Lee’s forces were in PA, and the belief was they would try to attack Washington from the NW, so it made sense not to advance too far north.

Reynolds clearly understood that Gettysburg had favorable terrain and ordered Oliver Howard’s corps to join him there, rather than fall back to Pipe Creek. After Reynolds was killed and Winfield Hancock arrived at Gettysburg, he confirmed Reynold’s decision to fight there rather than fall back. That was good enough for Meade, who abandoned the Pipe Creek line and moved up to Gettysburg.

It’s worth noting that a similar process was happening to Lee’s army. Buford had engaged Devin’s brigade (Hill’s corps), which was the vanguard of the Army of Northern Virginia. Lee had to quickly bring his three corps together at Gettysburg. Both he and Meade benefitted from the many, many roads that led to Gettysburg like the spokes of a wheel.

Essentially, yes. There are variations on this based on the time period (and thus technology) as well as the theories of any given army. But broadly speaking, a vanguard could be any given army unit that is simply assigned that task. The next time they advance, it could be a different unit serving as the vanguard. Some armies might prefer to make the same unit the vanguard on a regular basis and train/equip it differently because of that. In some instances, it might be sending horse cavalry out ahead of the infantry, or it could be a specialized tank unit in WWII. I tend to think in the context of the American Civil War, so I typically picture infantry units ("skirmishers"). Usually they want to clear out any enemy units separated from the main enemy force (stragglers, scouts, or the enemy vanguard). Depending on who intends to go on the offensive, the vanguards might engage each other in a minor "battle" but they are never intended to carry out a proper fight, only to "feel out" the enemy, get them to retreat to avoid the main force, prevent the enemy from gathering intelligence about the size or position of the main force, or like I said before to coax the enemy into an attack on an entrenched main force.

This, and by the 1930s mass media made it possible to disseminate propaganda to a wide audience. Photography, film, and radio were powerful.

Sending a smaller unit out ahead of the main body is primarily done to locate the enemy and scout positions. A smaller unit is more mobile and can fall back to the main body. Sometimes you want your enemy to chase the vanguard as it retreats so that your main force can then attack the enemy from favorable ground. Very commons in Napoleonic and American Civil War era tactics, though you still see good examples of it in the world wars.