How much did an, for example, divisional commander know about where the parts of his division were during a battle?

Generals often stood on high ground far enough from cannon fire but close enough to see everything and watched the battle unfold. When no such position was available, they'd have to manage the battle from reports which were sent back from the commanding offices in the field.

How detailed was this knowledge? Time was of the essence during a battle. So, often information flowing to and from officers to the commanding general were often very brief. Obviously, when the General had a direct view of the battlefield, their knowledge of the action was pretty comprehensive.

I'm unsure on Picket's knowledge of location of individual regiments prior to the charge but regardless, they tried to run across a huge field. He had clear visibility to what was happening once that charge started.

What if he wanted to know about where they are? How would those messages get sent around on the battlefield?

Messengers were constantly travelling between generals and commanding officers via messengers on foot and horseback. These were often not dedicated messengers but just the solider who happened to be closest by and asked to pass a hand written message.

Top Generals like would have several Generals beneath him. They would have several colonels then majors, then captains, then lieutenants, then sargents then the privates. Information flowed verbally up and down through a chain of command.

Also, how/if at all would smaller formations report about their position? Many officers had maps and reported their location against those maps. Often, there would be confusion as to exact locations of the troops as there was obviously no GPS at the time

Would, say an regimental commander report his location to his brigade commander?

Normally, it was the other way around. Commanding officers told their subordinate officers where to go.

You didn't really ask the question but I'd just like to add that in general, communication was very poor compared in the Civil War compared to what modern armies behave. Even when communication was possible, it was slow. There are many famous Civil War battles where there was confusion on the field, poor timing between divisions, entire divisions who didn't engage in battle, and ultimately, battles lost mainly due to poor communication. So, to deal with this, the Generals normally surveyed the potential battle sight prior to the battle taking place. They decided how the battle should unfold and they issued detailed orders to the chain of command beneath them. During the battle, all the officers knew what to with the assumption there would be an inability to communicate.

But on the flip side of the coin, communication was quite advanced in the Civil War versus all previous major wars. Wherever the Union army went, they laid telegraph wires. Hundreds of thousands of miles of it. The Commander in Chief (i.e. Lincoln), and the top Generals were able to directly control the entire Union army in a very strategic sense. Sensitive messages were encrypted to avoid intelligence leaks. The Confederate army used telegraphs as well.

You also didn't ask about how enemy force estimates and locations were communicated to the Generals. Spies, pickets, scouts, and lookouts were used to find these troops and report on them. They usually traveled by foot or horseback to pass on communications. Often the information was untrustworthy and ignored. When lookouts were in a good position, they could use flags as a communication method.

The source of my information is Grant's and Sherman's memoirs where they discussed how battles unfolded.