This is authentic. It is noteworthy to say that the translation is wrong and it is not “after the obligatory prayers” as this is an innovation. The correct translation is: “at the end of obligatory prayers”! This means before Salam.

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If he says it but in a low voice, the prayer is valid but it must be brought to his attention to stop such a practice.

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Yes no problem. Since it is last third of night you can ask plenty of duaas and this is the time of seeking forgiveness.

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No, it is not permissible and it doesn’t count. They do this in prayer, their prayer is invalid.

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