-snip- lets say online pc is compromised is it possible to extract by anyone private keys form the signed transaction file.

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This is fully answered but I would like to add an example why this wont happen.
That signed transaction file contains the same data stored in the blockchain and can even be queried using a blockexplorer using an address, TXID, etc.
So if it's possible to extract the private key from the signature, every unspent transaction in the blockchain should've been stolen by now.