Velho's post in Infield fly rule was marked as the answer
Since the batter is out with the Infield Fly, no runners are forced to advance. Since the ball was not caught, any outs would have to be tags. (If it had been caught, appeals for leaving early would be possible).
As described, the runner on 3rd base ('R3') advancing and touching home plate before she was tagged would be safe.
Velho's post in Is R1 out if he/she never leaves 1B bag on this play? was marked as the answer
You have it correct.
A hit, fielded by 1st baseman, tag R1, then tag the bag is a double play
A hit, fielded by 1st baseman, tag bag, then R1 is batter out. R1 safe.