#1 - I'm actually not sure. If your barracks is level 1 and damaged, it will stop producing. But I can't remember if there is any impact if your level 2 or higher barracks is damaged. Usually, later in the game, I have so many barracks that it doesn't matter if one gets damaged, so I never really pay attention.
#2 - The AI hates you because you've declared war on other countries and taken land and gotten powerful. Going to embargo first then declaring war doesn't make up for you invading six countries and having a large army. But don't worry -- it really doesn't matter much if the AI hates you.
#3 - It depends on the situation. Going all out on economy could pay off in the long run but you might regret it if you are attacked early. Going all out on units and early invasions might net you early conquests, but you might regret not having invested in your economy when you run up against the guy who had lots of time to build up.
#4 - Destroyers have no ranged attack like cruisers and battleships, but can still end up in a land battle with a land unit if the destroyer and the land unit are right on the coast.
#5 - Transport ships fight using their "vs. Ship" attribute, which is 0.8 if they're level 1. Of if they're fighting subs, they use "vs. Sub" which is 0.5 at level 1.
#6 - Yes, they are most likely multi-accounting. Not sure if it is worth the time reporting it.
#7 - The ratio of damage you give out and take should be the same as if you directly attacked. While patrolling, you give and take half the damage each attack, but you get more attacks per hour than if you directly attack. You'll end up doing (and taking) more damage using patrols than regular attacks, because patrolling is continuous, while direct attacks require your planes to return to base and refuel after every attack.
#8 - Look for BMfox Call of War on YouTube