Party Crasher is wielding a Chainsaw. Deliberate foreshadowing, or happy coincidence?

I’ll (seldom) admit to things being a coincidence.

If I attack the monarch with my creatures and they attack me with their party crasher, and neither of us blocks, then who ends up being the monarch at the end of turn and why?

All the damage happens at the same time, so the Monarch moves from the player that has it to the opponent.

If my opponent attacks me with all their creatures and I attack them with my party crasher, is my party crasher attacking alone?

Yes. “Attacking alone” cares about your creatures.

Silver-bordered rules question! If I'm in a three-player game, and I control a Party Crasher, and it attacks Player A during Player B's combat step, but Player B is also attacking Player A, and Player A is currently the monarch, then who between me and Player B gets to become the monarch by doing damage to Player A?

The person with the Monarch gets to choose which one gets it if the exchange is at the same time.

Un rules question: Party Crasher and Exalted. If I attack with my Party Crasher while my opponent is attacking with only one of his own creatures, does Exalted trigger for either of us?

His creature as he controls the Exalted creature and he is only attacking with one creature.

For trying out some new mechanics for red, what about implementing rules where red creatures can attack on any turn?

You should check out Party Crasher in Unstable. : ) Nowhere close to a thing black border can do.

Do creatures that attack from graveyards with Over My Dead Bodies stay tapped in the graveyard until my next turn? Or do they reset after combat so a dead Party Crasher could attack every turn?

They untap during your untap.

If I steal my opponent's Combat Phase with Clocknapper, but they control a Party Crasher, can it attack during the combat I stole from them?

Yes. It can attack during anyone’s combat.

Party Crasher: how does a creature that's both attacking and blocking assign combat damage? If it isn't blocked, does it have to deal damage to the creature it's blocking before the player? Does it get to deal damage to both?

If it is both blocked as an attacker and blocks as a defender, all damage in combat is done at the same time (save last strike, first strike, double strike and triple strike).

I don't understand your earlier answer regarding Entirely Normal Arm Chair and Party Crasher. Entirely Normal Arm Chair says I can put it onto the battlefield at any time during my turn, so if party crasher is attacking on my turn I can put it into play and then sacrifice it to kill Party Crasher.

I answered it poorly. Let’s try again. Your opponent attacks you with Party Crasher during your combat. You have an Entirely Normal Armchair in your hand. It’s your turn, so you can hide it on the battlefield. Note if you don’t try to hide it, it’s an illegal play. You then can pay 2 and sacrifice it to destroy Party Crasher. There is no window where your opponent can bounce it so you destroy it. So, assuming you make an attempt to hide the Armchair, there is no way for Party Animal’s controller to stop you. If the Party Animal’s controller figures this out ahead of time (you tried playing the chair earlier and they bounced it), they can always attack with it during their turn like a normal creature.