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In a game where you have only one opponent remaining, you would win the game before you can lose it. With more than one opponent remaining, both you and the targeted opponent would lose.
Losing due to trying to draw from an empty library is a state-based action:
704.5. The state-based actions are as follows:
704.5b If a player attempted to draw a card from ...
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You will still lose, even though your library will not be empty when you lose.
You will fully resolve Brainstorm, including drawing as many as you can from your library (none in this case), and then putting 2 cards onto your library. After Brainstorm resolves, state-based actions will be checked, including this one:
704.5b If a player attempted to draw a ...
6
Your opponents are mostly right.
What you're missing with this scenario are: combat steps, assigning damage, and triggered abilities.
When anyone attacks with creatures, there are certain steps that are taken. In general they are:
Before Combat
Declare Attackers
Declare Blockers
Damage
In each combat step, the action is only taken once. In other words, ...
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I'd say the realistic answer to the question is "those terms are not commonly used". Looking back through some recent tournament decks on the official Wizards site:
Simon Görtzen's Boros-splash-blue-splash-black deck at the October 2020 League Weekend is simply described as "Four-color Cycling"
All the Temur-splash-white decks in the Top ...
4
No
702.82. Exalted
702.82a Exalted is a triggered ability. “Exalted” means “Whenever a creature you control attacks alone, that creature gets +1/+1 until end of turn.”
702.82b A creature “attacks alone” if it’s the only creature declared as an attacker in a given combat phase. See rule 506.5.
Exalted triggers when you attack, and then after the trigger ...
4
No, each permanent individually can be tapped or untapped; tapping or untapping a permanent does not tap or untap any enchantments on it. Similarly, tapping or untapping an aura enchantment does not affect the permanent it is enchanting.
110.5. A permanent’s status is its physical state. There are four status categories, each of which has two possible ...
2
No, you have no opportunity to tap your opponent's creature after they have decided to pay the {3} to attack, but before they are already tapped and attacking.
The choice to pay mana is done as part of the declare attacker steps; they actually tap their own creature as part of attacking with it right before they pay the {3}, and you don't get priority to do ...
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Player B gets to choose exactly which of the 6 damage is prevented.
The two creatures deal damage simultaneously. Rule 510 deals with the combat damage step, and days among other things (emphasis mine):
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action
doesn’t use the stack. No player has the chance to ...
1
Nine Lives second ability is a prevention effect not a triggered ability:
CR 615.1a Effects that use the word “prevent” are prevention effects. [...]
When there are two Nine Lives on the battlefield, the interactions are resolved according to:
CR 616.1. If two or more replacement and/or prevention effects are attempting to modify the way an event affects ...
1
Several years ago there was a Jeskai deck splashing Black which players christened "Dark Jeskai".
Nonetheless, as Philip Kendall wrote, the names are not standard, and "four color" is the most common way to describe these decks.
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Your opponent is mostly correct. Blockers are declared all at once and once declared can't be changed unless cards specifically say to do so (like creating a token that comes in blocking like Flash Foliage or removing the creature from combat with Labyrinth of Skophos). The rules for blocking are section 509 of the comprehensive rules:
509.1 First, the ...
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