"-her" adds a notion of motion towards the speaker. In this example, it doesn't matter much since in both cases it means someone should sit down near the speaker; you would probably use hierher, but hier can be used if the person is already present at the place he is supposed to sit.
But you would make a difference between "er ist hier" (=he is here) and "er kommt hierher" (=he comes here/this way). You can't change them around.
Kind of like the difference between "Please sit here," and "Please sit over here?"
So is there a distinction between "Er kommt hier" and "Er kommt hierher" as in he's coming to the party but not here yet, vs he's already at the party but is now coming over to where I am?
No, "er kommt hier" is not a sentence you would say. "kommen" already requires a motion towards you, so it can only be combined with "hierher", regardless from where he starts this motion. In both your situations you would say "er kommt hierher". In the second one, to express that he already is close, you could also say "er kommt (he)rüber" (note that the r needs to be there as a short form of the her- prefix).
Capital Sie is the polite "you" to any number of people. Capital Ihr is the polite "your". Lowercase ihr is the informal "you" to more than one person.
In this case, the reflexive "setzen Sie sich" sounds a lot like what we might say colloquially (in American English at least): "Sit yourself down! "
What confuses me the most is that "Sie" should be "she or them" however in all the examples it seems to be addressing a "you" in an instruction or order! What is the deal here?
It's an imperative, and Sie with the upper case "S" means "you" in the formal sense.
Similar inherent meaning (although leaving out the part where it specifies "here"), but different grammatical construction. Overall, not close enough as a translation. Remember, that just as you can word things differently in English, you can too in German. Your sentence probably better translates as something of similar meaning but grammatically different in German.