Prayer

He should take it out. If he is unable to do that, he should keep it in his mouth without chewing it.

No, you don’t make up for these prayers as their time was gone and you missed them without a legitimate reason.

Yes.

If it was done unintentionally and without distorting the meaning, I hope that it is OK.

No one has ever disputed about Juma’ah prayer. it is 2 khutbas followed by 2 rak’ah prayers.

Probably they have an illness in their backs

This athan you hear is exactly the same athan that was at the time of the Prophet salla Allahu alaihi wa sallam.

From Hudhayfah – that performed prayer with the Prophet (Sallallāhu ‘alayhi wa sallam) and he used to say between the two Sajdahs: ”‘Rabbighfirli, Rabbighfirli’ (O my Lord! Forgive me, Forgive me). [Ibn Mājah with a hasan sanad]

It is permissible to pray your night prayer in the format you stated. If sunrise is at 5:19, praying fajr at 5:00 is too late and you have to pray it earlier.

You can pray as many rakkah you want providing that you do not perform another witr.