with the seed, I used Iancoleman with another computer (never connect to the internet) to get the address, private key, and that path m/84'/0'/3'/2.
So, just to be clear, you set up a new wallet using your Ledger Nano linked to Electrum, then took the seed of that wallet, entered it in to Ian Coleman, spun up this weird derivation path, and sent coins to it? Unless you are
completely certain that you have properly airgapped the computer you used, then I would consider that seed phrase compromised.
with that seed I'm split my balance into another path m/84'/0'/1'/1, m/84'/0'/2'/2, m/84'/0'/3'/2 ... get the address and keep private key, I haven't a problem with those all, I write down all the detail, and just confused to connect with those path.
The only one of those three paths which will be recoverable using your Ledger Nano and Electrum will be the first one, following the steps I gave above. The other two do not follow the BIP44 standard and so are not recoverable using either Electrum or Ledger Live. I'm not sure of any software which will connect to a Ledger Nano and let you open wallets at arbitrary paths like these. If it were me, I would be importing those private keys to an airgapped Electrum wallet and sending the funds on them back to my hardware wallet under a standard derivation path.
In future, if you want a different account, then open a new wallet with the same Ledger Nano and Electrum, only changing the third number in the derivation path. For example, m/84'/0'/1', m/84'/0'/2', m/84'/0'/3', and so on.
derivation path over 1 is not standard, for example, m/84'/0'/2'/1 ?, we must be careful about that.
A full derivation path for a specific address might look like this: m/84'/0'/2'/1/0. This is broken down as follows:
84 - Purpose. Essentially tells us that it will be a segwit address.
0 - Coin type. Bitcoin main chain (i.e. not testnet).
2 - Account. The third account.
1 - Change. 0 for receiving, 1 for change.
0 - Address index. The first address.
So, when you create a new wallet (which is an account), you should only specify the first three numbers - m/84'/0'/2', in this case. The last two numbers are different for every address in that wallet.
m/84'/0'/1'/0 - this is the first 20 address on electrum (no.1-20)
Almost. m/84'/0'/1'/0/0 through m/84'/0'/1'/0/19 will be the first 20 addresses in the second account.
when path m/84'/0'/1'/1 the next 20 address (change address-yellow mark-no 21 until number 40)
m/84'/0'/1'/1/0 through m/84'/0'/1'/1/19 will be the first 20 change addresses in the second account.
when path m/84'/0'/1'/2 my assumtion hidden address on electrum (no.41 until number 60), correct me if i wrong.
Electrum will never generate addresses at this path, since as explained above, it is non standard.