Dzien Dobry Kasia...
All major chords are built from the major scales.You know that the pattern for major scales is TTSTTTS.When you want to find the chord for a note(F) you must first build the major scale of that note(F).After you do that you must then choose the 1-3-5 of the scale to get your major chord.So the 7 for the F major scale is the E as you said and it is a half step under/before the root...I am sorry but this is all I can do to help
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All the best,
Theo