Is it permissible to renew a marriage contract over the phone with the wife's father who resides in another country? And what are the available options for that? And what about the location of the witnesses to ensure the contract's legitimacy and eliminate doubts?

For a marriage contract to be valid, both spouses must be specified. If the woman is present, pointing to her is sufficient. If she is absent, she must be named or described in a way that distinguishes her from her sisters. If the wife is not present at the contracting of the marriage and is not mentioned in a way that distinguishes her, then the contract is invalid, and you both must repeat it. She must also observe hijab in your presence. It is permissible for the contract to be conducted with her father over the phone, as long as your voices are clear and the witnesses are able to hear you both.