There are three possibilities.
This is a scam, as others have pointed out, it works by you sending money, then them stopping the original transfer, meaning you sent them your money and not theirs. They make money cause a stop payment only costs $50 (or around there) but you sent $1,000. So they profit $950. You lose $1,000 and maybe some processing fees.
This is money hiding, or money laundering. They send you $1,000 in drug money, you send them $1,000 in "clean" money. You don't lose any money. But they gain a clear paper trail. With large sums of money (in the U.S. anything over $5k) you have to prove a paper trail. They just did. You gifted it to them. On your end, it looks like you just profited from illegal activity, which in the worst case ends in confiscation of ALL your assets and jail time. It might not come to that, but it could.
This was an honest mistake, by an idiot. It is possible to wire a complete stranger money. If you make a mistake on the wire transfer forms, and the account number exists, it will go through. Now what makes the sender an idiot is not the mistake. We all do that. It's the fact that banks have a built in system for handling these mistakes. Simply put, you can make a stop payment. It's around $50 (varies by bank and sometimes amount transferred), it's easy to do, and almost automatic. If you tell a bank rep that you made a mistake they will likely have you fill out a paper, and in many cases will "just take care of it". If "the idiot" didn't want to tell the bank of the mistake, or didn't ask for help, or didn't want to pay the fee. Then maybe they would contact the receiving party. But that's pretty dumb.
The resolution in all cases is the same. Visit your local branch, or send in writing, an explanation:
"I found $1,000 in my bank account that I didn't put there, and got this email (see attached print out). Please advise."
They will "freeze" the $1,000 (or maybe the account but I have never seen that) while they investigate. You won't be able to spend it, they might even remove it pending the investigation. They will contact the bank that issued the transfer and attempt to sort things out. You shouldn't be charged anything. You also won't get to keep the money. Eventually the bank will send you a letter stating what happened with the investigation. And the money will vanish from your account.
I wanted to state the information above even though it doesn't address your concerns directly because it is important. To address your specific questions:
Question 1) Surely bank account numbers have a checksum, which make it relatively difficult for a typo to result in a payment going to the wrong person?
Nope, that's up to each bank. Usually the account numbers are not sequential, but there is no "checksum" either. Just like credit cards, there are rules, but once you know those rules you can generate fake ones all day long. In some cases, account numbers 5487-8954-7854 and 5487-8945-7854 are both valid. It happens.
Question 2) What are likely sources of them being able to find my phone number to call me?
Phone numbers are not private. Not even close. Phone books, Google, Websites, etc etc. if you think your phone number is in any way a secret then your totally misinformed.
Account numbers are not a secret either. Especially bank account numbers. You could totally just call a bank, and say "What is the name on account 12345?" and they would tell you. Checks have your name and account number on them, as do MANY documents from a bank. So anything from asking the bank, to finding a copy of a check or document in the trash are valid ways to make the link.
Question 3) How were they expecting to benefit?
See options 1 and 2 above. If is is really option 3, then your bank should have directed the money back. But if the person was so messed up as you say, the account may have been closed and "written off". When that happens a lot of weird stuff can happen. Essentially the bank is "taking a loss" of money and doesn't want the money back even if the account was closed with a negative balance. Usually though contract with debt collectors, they may have already been "paid" for that debt, and are not allowed to take the money back. These things happen, but it seems like a pretty odd set of things that need to line up for #3 to be valid.
About your Length of time
Usually these things resolve in less then 90 days. Usually far less. At the 90 day mark, it gets really hard to reverse a transaction. It's possible that it was a scam and so many people fell for it that the scammers just let you keep the money instead of "highlighting" their scam. The fact that your using a "net bank" means that your can't go in person, but you should get details in writing. State the transaction number (it should be in your account records) and ask them for a "letter of resolution" or some form of official document stating the outcome of their investigation. I suspect that no one every really investigated the issue and the rep you spoke to never did anything then ask you to ask them to fill out a stop payment.
You need a record of trying to sort this out. You don't want to up for some legal battle 10 years from now because someone found out that the money was part of a pool that was used to fund some terrorist group or some such. So get a paper trail, then go with what the bank says.