Question 2: Why would a transaction ever have change that needs to be returned to the sender? With BTC can't I give a vendor exact change every time, so that he'd never have to give me anything back?
Bitcoin can only create transactions by using as the input an ENTIRE prior unspent output. The most important thing to realize is that Bitcoin tx have inputs and outputs. The "value" of your wallet is an abstraction. It is simply your client (software which analyzes the wallet) taking a SUM of all the unspent outputs which you have private keys for. The input of a tx is the output of a PRIOR tx. You can only use unspent outputs in a new tx. Once they are part of a tx they can never be used again ("spent").
Say you I send you 50 BTC (for simplicity lets assume this is compromised of a single 50 BTC output). No matter how you spend that the input for the tx will be 50 BTC.
Want to spend 20 BTC? Input: 50 BTC Output: 20 BTC + 30 BTC "change" back to an address you control.
Want to spend 1 BTC? Input: 50 BTC Output: 1 BTC + 49 BTC "change" back to an address you control.
Question 3: If the only difference between this chart and the one above is the removal of "change", why is the shape of these charts so dramatically different? The huge difference makes it seem like the change that is returned to the buyer is comprised of MOST of the money that was initially transferred from buyer to seller. It seems kind of like an equivalent real-world example would be me giving every cashier at the grocery store 5 times as much cash as is needed to cover the cost of my groceries... and then she gives me most of the money back. This doesn't happen most of the time in real life, so why would it be happening most of the time with BTC?
In the early days of Bitcoin there really was nothing to "spend" it on so most tx tended to be accumulation. This resulted in most addresses having very large unspent outputs. As people started "breaking" up those unspent outputs in tx involving smaller amounts most of the volume WAS change.
Nice observation.Forget the crypto lets think about it in physical terms that might make it easier.In the physical world with fiat say you want to buy a soda at the store for $1.25. You open your wallet and the only bill inside is a $50 one.
How large will the tx be? $50 right? Input: $50 from your wallet. Output: $1.25 to merchant's "wallet", $48.75 back to your wallet. Now in the fiat world your $48.75 is compromised of multiple fixed denomination bills & coins. Only the central bank can issue currency and they issue them in a few fixed size denominations.
Now imagine the physical world worked like the Bitcoin protocol. In Bitcoin the outputs (i.e. $1.25 to merchant AND $47.75 back to you) become new "bills". Hypothetically the merchant would destroy your $50 bill and in the process print a $1.25 bill for himself (not a dollar and a quarter but a single $1.25 bill) and a $47.75 bill for you. Your "change" wouldn't be a bunch of fixed denomination bills it would be a newly printed bill for exactly $48.75.
Why doesn't the fiat world work that way? Well the obvious reason is trust. A merchant could cheat and destroy a $50 bill and make $100 or $1,000 worth of new bills. The bitcoin protocol prevents that. Miners validate tx and put them in blocks. Those blocks will be rejected by other miners if they are invalid. If you have a tx which has $50 input and $50.00 + $1.25 output it will be invalid. If the tx is invalid the block is invalid. Since miners get compensated for good blocks added to the blockchain they have an incentive to reject bad tx.
Now all these examples have involved a single input for simplicity but they don't have to. Say I give you a $28.75 bill. Your wallet now has two bills one for $48.75 and one for $28.75 (in Bitcoin we would call these unspent outputs). If you wanted to buy something which was <$28.75 you could use either bill. If you wanted to buy something more than $48.75 you would need to use both bills. If you had lots of bills you could choose the ones which closest matches the change to make it small (or possibly nothing).
