"Now to [1], unconfirmed change. You have received a ~0.9 BTC bill and want to use it. In order to use it, you have to use it entirely and send the rest back to yourself as change."
This^, under normal cicumstances you dont have to worry about change or how it works. Your wallet software will take care of that. When you look up the transactions in a blockchain explorer you will see a second output. Its like you send the coins to two persons. E.g. here
-> https://blockchain.info/tx/be928ef28f9bc65643a33015b85a2d03971950b0da62cf8e9ff8353c0f2f5c55?show_adv=true (I turned the "advanced" mode on, by clicking on "Show scripts & coinbase")
On the left side is the address you received the coins on. On the right side are the two(!) addresses you send coins to. One starting with 1KF sending ~0.05 to someone else and one starting with 1KP sending ~0.86 back to you. Note that I only know which address is yours and which address belongs to the other person because you told me so. There is nothing within the transaction itself that allows me to learn which of the two addresses are yours.
If you click on the little red "spend" you can follow the coins and see where they have been used following this transactions. Now the address that was just on the right side appears on the left side as input. There may be more inputs and there may be 1, 2 or any larger number of outputs (right side).
Only one output is very rare, because it usually means that you can send coins without change. Lets assume you have received several transactions in the past that you can now use as inputs. E.g.
2x 0.1 btc
5x 0.05 btc
1x 1.75 btc
Now you want to send 0.3 btc (we ignore fees to keep it simple) and if we look at the inputs we can use both 0.1 btc inputs and two 0.05 inputs to have a total of 0.3 btc. This is usually not how you receive bitcoins though. More often you receive coins they will be like the transaction you received recently or the once you created, using all (or almost all) 8 decimal places. Chances that you have the exact right combination of inputs ready are very slim, so a change output is almost always created by your wallet.
.... that might have been a bit too much for starters, feel free to ask questions if you have any.