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zaps forwarded to @k00b (100%)
If I made 1000 deposits to my Electrum wallet, each time using an unused address, and then recovered my wallet by seed phrase on a new device, would it accurately display my balance?
If not, how could I get it to display the true balance?
Also, how can I send funds from an electrum 12 seed word wallet without connecting it to the internet?
Yes. And that is true for 1000, 10000, 100000, or any number of transactions, since your wallet is deterministic, that is, it will create the same addresses in the same sequence, every time. As a matter of fact, you can now install an Electrum wallet on a second device (one on your laptop and one on your phone, for example) using the same seed phrase and see for yourself that the addresses generated in both are exactly the same. One of them could even be watch-only, that is, you won't be able to spend from it, only see the transactions.
To spend your BTC, you need to create a transaction, sign it, and broadcast it to the network. Those steps can be done in the same device or in different ones, and only broadcasting needs to be done online.
You can create and sign a new transaction on an offline device (even air-gaped) with your Electrum wallet, where your keys are stored, and then transfer that transaction to a second device, with a second Electrum wallet, which doesn't need to store your private keys (it can be a watch only wallet, or not even that), to go online with and broadcast (make public) the transaction.
That is an interesting and fun experiment, and it helps to understand how Bitcoin works, and it also gives you the peace of mind to see for yourself that the recovery system will work. If you don't want to use a second device, you can also create a second Electrum wallet (whether standard or watch-only) in the same device using the same seed phrase. It's not as cool as having two identical wallets in two different devices, but it serves the same idea.
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Can I create a transaction in an offline electrum wallet that has never been online before and displays 0 as the balance, even though the balance isn't zero, and then broadcast that transaction to the network using an online HTML broadcasting tool?
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I'm not sure about that, I haven't tried it myself.
What I've tried, though, is creating the transaction on an online watch-only wallet, transfer it then to an offline air-gaped wallet in a second device, sign it there, and then transfer the signed transaction back to the hot wallet to broadcast it.
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You could create a watch-only wallet so that your private key is always offline. I would recommend creating another wallet, since this private key has already been in contact with internet connected devices.
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If I understand correctly what you describe, yes. You should be able to recover everything on a new device. That device needs to be connected to the internet to connect to a full node to find your balances. You need to be connected to the internet to send funds after recovering
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