During a battle, what happens when the BP of the attacking character and the blocking character are the same value?

During a battle, what happens when the blocking character's BP is greater than the attacking character's BP?

When I perform a trigger check on multiple cards simultaneously and some revealed cards have triggers and some don't, am I free to resolve trigger abilities on cards and place cards without triggers into my sideline in any order I want?

If I deal 2 damage to my opponent with ▼Damage (2)▼ when they have 2 life and performing a trigger check on both cards simultaneously reveals one of them has a Final trigger, does it activate? How do we resolve it if both cards have a Final trigger?

When a trigger ability activates, do the other abilities on that card activate as well?

If I am performing a trigger check and a character is played, do [When Played] abilities activate? If they do, is the trigger check still in progress while I am performing them?