Yes it will 1 backup is enough
ok great thanks! i thought I had to backup each time I made transactions or something.
One more question. Say I backup the wallet.dat with 10 BTC, and simultaneously use a separate PC, download new Bitcoin wallet and replace that with the backed up wallet.dat.
Obviously they cant both show 10BTC balance ... will it error out since that wallet.dat is in use already?
All the value is stored in the blockchain that every full node on the entire network has a full copy of. The wallet is just a list of private keys (think of them a bit like passwords) that allow you to control some of that value in the blockchain.
If you log into a bank website and create an account, funding that account with $100, and then you log into that same bank account from another computer, it will show the $100 as well, right?
Similar concept here. Both copies of the wallet will see the same 10 BTC balance. If you spend some of that 10 BTC with one copy of the wallet, that value will vanish out of the other wallet as well.
This is why a thief doesn't need access to your computer or your wallet to steal your bitcoins. All they need is the private key of the address that has some unspent bitcoins associated with it. They can then import that private key into their own wallet and spend your bitcoins. The bitcoins will vanish from your wallet.
Note that it is a very bad idea to try to run 2 identical copies of the same bitcoin wallet. The Bitcoin-Qt wallet software will generate new bitcoin addresses that it will keep hidden from you and will send some "change" to these additional hidden addresses when you send a transaction. Eventually the two wallets will have a different set of "change" addresses. Then each wallet will show a different balance since they don't have the private keys for the change addresses that were created by the other copy.
