No there is no framing rule.
No, in no level of softball or baseball can you use your helment or hat to catch a ball
No if it is a foul ball or if it hits the fence and you catch it it does not matter you still can play it if it is not foul but if it is foul and you catch it when it hits the fence they just call it a strike. Actually - you CAN catch a ball off the fence. There is no rule against it, however it will NOT be counted as an out. The fence is part of the field just like the ground. Therefore, if it hits the fence in foul or fair territory, it is played the same as if it had hit the ground before you caught it.
you catch and throw a ball
If you have to ask you probably shouldn't play.
If your at a baseball or softball game and you catch it in the stands it does not count as a out and you can keep the ball
No, but there should be.
with a baseball glove and to throw it use your bare hand
7 innings unless there is a mercy rule
There are many rules in softball but there are different leagues. Post a question more specific about what type of league and you may receive better answers.
I assume you are referring to the international tie breaking procedure. It can be used as a state adoption. Please check with your states high school athletic association to see if they have adopted the rule.
softball has 7 innings in less a tie then they play more innings if one team is winning by a lot they have the mercy rule and they call the game