I don't know about being smart enough to answer that question, but it might help to be somewhat clarivoyant.
As the question is stated, we have to assume that the throw home was in sufficient time and accompanied by a sufficient tag to retire R3. If that is the case, then that would be our second out.
For the subsequent throw to first, we need to assume that the batter-runner interfered with the fielder- if there even was one!- receiving the throw before we can assume the B/R out for interference.
And if all those assumptions are correct, no runs would score on this play as the third out was made against the B/R prior to him reaching first base.
But you've left out enough pertinent details that we could assume just about anything on this play. I could assume that the throw to the plate was late and R3 scores. I'll then assume that F2's throw to first was in the dirt and heading toward foul ground, not a throw likely to retire the B/R and thus not interference with the fielder taking the throw.
Now I'm going to assume that the defensive coach charged onto the field arguing for an interference call that wasn't there. Meanwhile, R2 and R1 continue running and cross the plate. The B/R makes it to third before the defense wakes up and realizes what's going on. The defensive coach is ejected when he calls the umpire a "blind *@#!%!".
So the obvious answer is: three runs score, there is still only one out, the coach has been ejected and we continue with a runner on third base!
