Is the marriage considered valid if the girl appointed her mother's husband as her guardian in the marriage contract, and she was unaware that the guardian must be the father or the paternal uncle? And what is the correct action to rectify this matter and remove the sin from the deceased and from her?

Marriage without a wali (guardian) is not valid according to the majority of scholars. The woman's guardians, in order of precedence, are: her father, then her paternal grandfather, then her son, then her full brother, then her half-brother (from the father's side), then their sons, then her paternal uncles. If the closest wali is absent, he may appoint someone else as his proxy, provided that the proxy is qualified for guardianship. Your marriage is not valid according to the majority of scholars, but there is no sin upon either of you as long as you believed the marriage to be valid. The child will be attributed to his father.