…Or just keep throwing penalties at them and hurting the team as a whole?
Yes. Here’s a recent article about ejections for helmet-to-helmet hits.
I don’t know how egregious an offense has to be to warrant ejection, but they certainly have the option.
But only for helmet to helmet, or can they send a guy to the showers like a baseball umpire can, just because they want to? I’m thinking specifically about the Ravens/Pats game from Monday where the Ravens player was hit with two Unsportsmanlike Conduct penalties. I was wondering if instead of assessing those two penalites he could have just told the offending player to take a hike.
Also, from that article: are all players in the NFL fined for the penalties that they do get?
I have seen players ejected for violent punches/stomps, and also once recently on a Monday night game for spitting in an opponents face.
Sure the Ref can eject them.
In a new rule, the coach can actually take a player out of the game if he is hurting the team as a whole. Or his teammates can take action themselves.
Of course, the option always exists to act like an adult and take responsibility for ones own actions.
I would imagine that if he had ejected him, they still would have assessed the penalties (certainly the first one). I imagine that ejections are reserved for certain flagrant acts (helmet to helmet) and for assaulting officials, but I have no cites to back that up.
But I don’t think an ejection negates the penalty that triggered it.
In college football (and I believe HS as well), 2 unsportsmanlike conduct penalties is automatic disqualification. As is fighting, punching, kicking, etc. The official also has the ability to disqualify a player or coach for especially flagrant personal fouls or unsportsmanlike acts.
The NFL does not carry automatic disqualification for any circumstance other than using the helmet at a weapon, but the official is permitted to disqualify a player for repeated uniform violations, fighting, flagrant personal fouls, contacting an official, taunting, abusive language, or other unsportsmanlike acts.
Disqualification is in addition to the distance penalty. If the distance penalty is declined, the player is still disqualified.
Can you explain this? I assumed the coach can “bench” any player at any time because that’s what coaches do. Same with baseball managers.
For example, before Our Lord and Savior Derek Anderson came to roost in Cleveland, our coaches had to remove and replace QBs all the time.
Is the “rule” different for quarterbacks? Do you have to set a roster and stick with it?
Fight my ignorance please 
I’m thinkin’ woosh on this one. 
Sort of. An NFL game roster includes 2 active QBs and a third “emergency” QB. The third QB can only enter the game if QBs #1 an 2 are injured.
Sometimes a non-QB will be the emergency QB (Antwaan Randle El when he was a Steeler, for example) which gives the team an extra roster spot.
I see nothing in the rulebook that indicates this. Any player with a number less than 20 can play quarterback at any time. You do run this risk that you are limited on the number of helmets that may have radios in them, so leaving your QBs on the bench may mean you have to signal plays the old fashioned way.
Ok I see (but not from the rulebook) that you can have an “emergency” QB among your inactive players that can dress and enter the game if the players on your active roster you have designated as quarterbacks are injured and can’t play.
Sean Taylor was ejected from a game for spitting in an opponent player’s face in the 2005 (06) playoffs.
Albert Haynesworth was ejected last year after receiving an “unsportsmanlike conduct” penalty for stomping on the head of another player, whose helmet had been knocked off during the play, as he lay on the ground. A more egregious foul, I have never seen. Obligatory YouTube video.
This is what I was talking about. The point is not that you couldn’t have someone else play quarterback, just that the “emergency” quarterback is a unique roster position.