"A man is eating."
It seems that ест is "to eat" and я меня естъ means "to have...."
Are the two words related, or is this just coincidence?
It is a coincidence. "Есть" is both the infinitive "to eat" and the present tense of "be" (быть). In modern Russian we only use the present tense of "to be" in special cases, one of them being "у ... есть ...".
And the difference between ем and ест? Is ем for you and I while ест is for he and she?
This is lovely for US Portuguese speakers, right? Russian has been so convenient to learn.