Conversion in the Rabbinate

Hello Rabbi Michael,
I wanted to ask you a question about conversion.
I have a friend in the army whose father is Jewish and whose mother is a Gentile. He recently joined the Nativ course (a course that prepares Gentile soldiers for conversion) and from there he continued to the advanced stages of the course and successfully completed them. He made an appointment at the Rabbinate's court for conversion this coming April.

I heard in recorded lessons from a certain rabbi that there is concern about the rabbinate's courts for conversion matters, that because they remove converts who do not intend to observe Torah and mitzvot, they are presumed to be a court invalid for conversion, so that even if a gentile comes before them intending to convert for the sake of God, and they convert him, the conversion is invalid (and all this without the court and the gentile being aware that the conversion is invalid).

My question is, is this indeed the case in terms of halakhah? And if so, is it better to send the friend who wants to convert to the Haredi Eda Beit Din?

Also, I assume that there have been a lot of invalid conversions in recent years, that no one is aware of the fact that they are invalid. Are the descendants of people whose conversions are invalid also considered gentiles? Or can it be argued that they are considered Jews by majority annulment (just as the descendants of an assimilated Jew are considered gentiles by majority annulment).

And another question, should a person be concerned about the invalid conversion of one of his mothers? After all, it is not improbable that one of the mothers 100 generations ago was a convert who may have had an invalid conversion.

Best regards,