#1
In the progression:

Em F Am C
F Am C E

Why is it that the switch from E minor to E major works? What is it called?
#3
Where did this come from? Do you have any context?

What came before and more importantly what comes next?

I would be surprised if that final E is a set up to go back to the Em which makes me think there's more to this than what you have described.
Si
#4
The E major chord is the dominant chord in the key of A minor. It is really common to use a major chord instead of a minor chord as the chord built on the fifth scale degree in minor. Both are used but E major has a stronger pull back to the tonic (Am). If you play Am chord after the E major chord, it will sound resolved - you have come back to the tonic ("home chord").
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

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