Situation 1) Calling "time" at inappropriate times is an example of poor game management skills. Time should never be called when there is continuous action, with runners advancing or before fielders have returned the ball to the pitcher.
Situation 2) If I was the coach of the offensive team on this play, I would have pressed this point with the umpires: THIS IS NOT AN INFIELD FLY SITUATION!
With runners on first and third, no matter how many outs, the IFR is not in effect. Result of the play should have been runner from third scores, runner from first out, batter-runner on first base.
The IFR can be called retroactively, though it is something that an umpire should avoid. If the umpire fails to initially call the IFR, and the offense is put in jeopardy due to a lack of a timely call, the umpires may place runners or call outs to rectify any confusion caused by their late call.
But this can only be done on plays where the IFR was actually in effect- and this play wasn't one of them! If protests were allowed in this game, your coach would have a protestable misapplication of a rule and this protest would be 100% winnable.
If this was an IFR situation (runners on first and second, or bases loaded, with less than two outs) a pop-up behind second might or might not qualify as an infield fly. That part is judgement on the part of the umpires. The fact that the ball was on the grass is irrelevant. If the ball can be caught by an infielder with ordinary effort, it can be on the grass.
Since that aspect of the rule is purely judgement, it's hard to say if this batted ball would have fit the definition of an infield fly, even with the requirement of which base the runners started out on being met. If the fielder had time to settle under the ball, but misjudged it or dropped it, maybe an infield fly. If the fielder was running for the ball, or had her back turned to the infield going out for it, maybe not.
All in all, it sounds like you had some inexperienced officials for this game.