Penalty Questions

[MagiCat]

USA Hockey question for a High School game:

Team A is up 5-3 with 4:30 left in the third period.

With 4:30 left in the 3rd period, 2 separate players on Team A get 5 minute major penalties and game misconducts. Both players were sent to their dressing rooms. Question number one is whether the teams need to put 2 other players in the penalty box under rule 404? Also, does this answer depends on whether the game can end up in a tie, have an immediate shootout if a tie, or have a 5 minute OT and then a shootout?

Continuing on, with 1:30 left in the 3rd period and the score still 5-3, a player from team A gets a minor penalty for tripping in their offensive zone. Given that the 2 major penalties are still on the board, this means that the clock on the minor penalty never actually has a chance to even start. Is there any other ramification to Team A besides their player being in the penalty box? Again, does this change based on whether the game can end in a tie, OT, or shootout? If there is no other consequence, it would seem that Team A could use this to their advantage by hooking, holding, or tripping someone every time that team B got possession the puck (kindof the way an NBA team will foul someone towards the end of the game if they have a foul to give without free throws.)

Lastly, assume that Team B scores 2 goals to tie the game and the game goes to a direct shootout (and assuming that rule 404 mandated 2 extra players go to the penalty box for the majors.) Would those 2 players be eligible for the shootout since they're serving someone else's penalty?

The first two parts actually happened in a game, the last part is just me imagining what could potentially have happened.