Finding a convenient time in the last few minutes to confirm with the scorer that there are no bookkeeping mistakes is an excellent idea. The officiating crew does not want to be hanging around on the floor at the end of a tight ballgame to make sure of this. When I have this brief chat in the last couple of moments, I always let the scorer know that I will make eye contact after the final horn and if all is good to give me a thumbs up or a head nod. This allows me to approve the final score and know that there aren't any mistakes to be fixed and also lets my crew get the heck out of there quickly.
As for your other question, my personal opinion is that the more information that you have the better job that you can do officiating the game. Therefore, I try to know how many time-outs each team has taken and of what type (our crew actually breaks this up: R has fulls for both teams, U1 30s for home, U2 30s for visitor), how many team fouls there are, what the score is, how much time is on the clock, and yes, even how many fouls there are on individual players. The last one is a bit controversial and opinions will vary. Mine happens to be that I want the extra information as one never knows when it could be important, such as when a scoring error pops up and the R has to make a decision.
Finally, I will again state that all of this info is for ME and my duties. I do not pass any of it along to the coaches and players. Nor do I normally let my partners know. That kind of info just overloads a lot of officials and doesn't help their game. So I don't burden them with it. If something comes up, I can be of assistance. Of course, I do have partners who are like me and we will share this info during the game.
So in summary, track all of the info that you wish during a game, but keep it to yourself.
