1) Is there any reason to save old wallet files if I'm generating a new backup after receiving some BTC?
Which wallet? If you are talking about Bitcoin-Qt, then it might be a good idea to keep a few of the recent backups in case the most recent backup turns out to be damaged or unrecoverable for some reason. The advice might be different if you are not using Bitcoin-Qt.
2) Is there even any reason to generate a new backup after receiving some BTC or does the wallet backup just contain the private keys associated with the public keys, and it will be the exact same file regardless if the balance is updated?
Which wallet? If you are talking about Bitcoin-Qt, then it uses a new address (and therefore a new private key) every time you send a transaction (although it doesn't tell you that it used a new address). It isn't necessary to backup after EVERY transaction that you send or receive, but it is a good idea to backup on a regular basis. This way you will be sure to have a backup of any recently generated keys/address, and you'll have multiple copies in case one copy turns out to be unrecoverable. The advice might be different if you are not using Bitcoin-Qt.
3) As I understand it, an offline/paper wallet saves the private key to paper, and this is required to send money from that address. Is this right?
Yes.
4) Is it wasteful to discard lightly used wallets?
If there are any bitcoins still in the wallet and you don't have any other backups? Yes. Otherwise, no.
5)Is there a place to recycle wallets that you no longer use?
If there are any bitcoins still in the wallet? Sure. You can email it to me.
6)If more than 21 million people want a wallet,do we get to pick who we have to share with?
No sharing necessary. Everyone gets their own wallet. There are plenty.
There are a maximum of a bit less than 21 million "bitcoins", but each wallet can hold fractions of a bitcoin.
I opened two different backups of the same wallet in notepad. Why are they different? Wouldn't they be exactly the same file if all they contain is the private key?
Which wallet? If you are talking about Bitcoin-Qt, then there is transaction information stored in the wallet.dat file in addition to the private keys, the bitcoin addresses, and any description you've added.
Is it an issue to have loads of addresses? I've got 7 at the moment labelled so I know who's paying me. Can I have hundreds of addresses if I want?
Yes you can have hundreds if you want. It is recommended that you use a new address for every transaction. This increases security, privacy, and anonymity.
This address is pulled from the client's pool of 100 addresses, so you should back up after every 100 transactions.
It would be better to backup
BEFORE 100 transactions. If you create 10 addresses, and then send 100 transactions, you'll likely have used 110 addresses. That means for the 10 most recent transactions you don't have a good backup and if your computer crashes, you could potentially lose bitcoins.
I'm not sure exactly why it works like this, I'm sure there's a reason.
It provides increased security, privacy, and anonymity.
Armory is a client which works deterministically, meaning that new addresses are generated in a pre-determined manner. This means you only need to back up once. It's also a great way to store coins securely, if you have a spare old laptop to run an offline wallet.
I agree. If you have the spare equipment and willingness to tolerate the slight increase in inconvenience, Armory is a great option.
Each time you generate a new address, it's totally random right?
Yes.
I know that the odds are against it but can an address be generated twice?
Realistically, no. But there is nothing preventing it beyond the astronomical improbability of it.
Seeing as you seem to like numbers, and I'm curious about it, what are the odds of that happening, and are there safeguards in place?
There are no safeguards beyond the size of the numbers.
If I generate an address, the odds that you could then generate that same address are somewhere around:
1/(2
160) = 0.00000000000000000000000000000000000000000000068% (6.84 x 10
-47)
(I may have one too many or too few zeros in there. I lost count).
That's approximately a 1 in 1,461,501,600,000,000,000,000,000,000,000,000,000,000,000,000,000 (1.46 x 10
48) chance.