Somehow I formatted the directory containing my secret key. But I still do have a sig file that was created using that key. Is it possible to somehow re-engineer the secret key from that? Or can I somehow sign another file using that one sig file?
Just imagine how much you could trust a signature if it would be possible that someone could create a mail signed by you just by having a mail which was originally signed by you. Therefore: while in theory it would be possible to correctly guess the private key it is impossible to do this in practice (i.e. will take way too long). And it would be very bad if this would be possible.