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If you are not on the network you cannot make transactions on the Blockchain. You are talking about something like off chain transactions, like the lightning network, where small transactions occur on a different network and are then bundled up onto the main chain. However this is on top of the existing network and requires ongoing access to the bitcoin Blockchain.

What you propose cannot work.

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As I understand it there is no central network. So nodes inside the firewall only see internal transactions. Nodes outside the firewall only see external transactions.

As a result, both sets of nodes create long chains based on the transactions they see.

Yes but the 2 chains cannot be merged, the longer chain is the true chain, so all the transactions on the shorter chain get cancelled. Essentially the users in the fire walled country would revert back to where their transactions and balances were in n they day they diverged. Good for some, not for others.

So if China firewalls and keeps mining they could take over the chain?

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