The things to remember about Rhino is: He's not very good at Schemeing, but since he only has one stage in the main scheme, he can complete it in one turn if you are unlucky. keep track of the "Advance" encounter cards. Use cards like "Emergency" or "Great responsibility" to avoid that. You could also try playing two heroes. That would double the amount of threat Rhino needs to win making it less likely for him to win in one round, but you still need to keep an eye on threat. He can hit VERY hard ! Rhino with charge can easily hit for 7+ Use cards like spidermans "Backflip" "ARMOURED VEST" or CPT. AMERICA "SHIELD BLOCK" to redoce or block the damage. Med team and Down time can help you heal afterwards

There is no upper limit in the rules, but since both your examples use a Power Action to roll in the extra dice, and the dice are set aside when resolved or removed, it's highly unlikely that you will ever need more than two. I have a Phasma + Mega blaster troopers deck that needs 6 First order Stormtrooper dice to be sure i always have enough.