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Is it possible/feasible to have a private key stored inside a smart contract and sign transactions with it or would the calculations be to pricey in gas?
For example a smart contract should create signed transactions and the costs should be not much more than the transaction cost itself

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If you store something in a smart contract, then anyone can see it. It's no longer private, so anyone can take it and sign something. So, technically, you could store a private key inside a smart contract and write the smart contract to sign transactions (which would be fairly expensive), but it would be expensive and insecure since anyone could grab the private key.

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I don't think it's possible. The essence of "private" key is that it is "private". You can write it down on a piece of white paper and keep it in a safe. The white paper should never go outside of your sight. The smart contract, however, is exposed to public eyes. Since everybody could see it, we can't call it a private key anymore.

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