It is permissible to offer salutation upon the Prophet salla Allahu alaihi sa sallam while in sujood as it is Duaa and Duaa in sujood is recommended.

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You were wrong in finishing the salat once you knew you were not in wudu. You should have broken it and made wudu to pray.

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Yes, but it is not recommended as it is distracting.

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This is not for you to decide. Only a Muslim ruler or judge can decide this. Kindly refer to the following link(s): https://www.assimalhakeem.net/what-is-the-ruling-on-calling-a-muslim-as-kaafir/

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