Can a user send a transaction using my website frontend with an account which is not in my node?
The solution to this problem could be create an account for every user in my platform, but I think that there should be some better solution.
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Yes. The user could send a signed Transaction to your website which can then be forwarded to your node. Take a look at Hooked Web3 Provider :
The Hooked Web3 Provider is a normal HTTP Web3 provider that allows you to "hook in" an external transaction signer that can be used to sign transactions for accounts not managed by the Ethereum client (i.e., aren't managed by geth).