It is until the start of the adhaan of fajr.

my question is in regards to tahajud/witr, is the end time for tahjud/witr just before the Azaan of Fajr or is it till you have started praying Fajr, for example if Fajr starts at 5:30 and sunrise is 7:20 and i set my alarm to try and wake up and read tahajud and witr and i wake up at 5:35 do i then have to do qaza of witr and pray fajr or can i read witr and then pray fajr

Prayer | February 23, 2017 4:17 pm
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In the very unfortunate event that I realize that my awrah is not properly covered while in the middle of a prayer, should I complete the prayer and then repeat it, or should I stop the prayer, fix the problem and then restart the prayer?
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I go to a public school and we are not allowed to miss or leave school on Fridays so we have come to terms with the school in which we will have approximately 20 mins to hold a Jumu’ah khutbah and salah, I wanted to know whether this is acceptable in islam inshallah.