Can a PC with Lucky reroll an enemy’s initial Grapple check?

How would you handle Intimidation/Persuasion through the Message spell?

For the Polymorph spell what counts as a “creature”?

Can a monster harm itself to break the paladins abjure enemy ability? …and a barbarian?

The Barbarians +2 damage when raging, does it apply to weapons such as the Dwarven Thrower when thrown?

Can you use warcaster to cast Eldritch Bolt as a Attack of Opportunity even if you’re level 5?

As far as improvised weapons go, how much weight can I throw, and how far?

Is magic explained anywhere in any official 5e books?