[fi:meil], I think I am ok
throughout - the vowel in the last syllable
I skipped t because of the afterward. Is this that made it sound incorrect for you?
underage - the vowel in the 1st syllable
got it
I may sound a little like ander
religious - there's no R in the last syllable
got it
wait - the vowel
got it too short
required, didn't hear the R in the last syllable
got it. Some I paid attention, some I missed it