ANSWER:

This applies only for the congregational prayer in the masjid. 

I know that we are not supposed to be praying the sunnah for before fajr while the fard has begun in the masjid. Does the same ruling apply for when we’re praying at home? If I am praying sunnah and my family starts fard, should I stop?

Prayer | June 21, 2020 7:12 am
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What should a person do if he joins the prayer when the imaam has alredy finished one rakat and at the end the person forgets that he had missed one rakat and finishes the salah with the imaam, does he have to repeat the whole salah or not?
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Can a sinful person lead people in prayer when others don’t want to lead? That person is involved in a serious sin of masturbation. Otherwise, he has a long beard and doesn’t lie and pray salat on time. Doesn’t cheat or consume Riba, also very dutiful to his parents and people around. Can he still lead prayer or he should avoid it? As others consider him very pious person.