1 - Battle Bonus are bonus to your Xp, credits and free xp. It is active when you do not see the timer. The battle bonus only apply to your next fight. You will see the bonus added at the end of the match during the progression part. When there is a timer, it indicate that you must wait that time before benefiting from the Battle Bonus. You can if you wish stop the timer and benefit again from the bonus by paying the indicated amount of credits. By doing so, on the long run you will gain more Xp but less credits.
2 - It depends of what you buy. Any Coating, Pattern, Emblem and Decal bought under the Appearance tab will only be unlocked for the current class and manufacturer. For exemple if you buy the "Orion Construction" coating for an Agosta, it will become available for the Trafalgar, Otranto, Vigo and Athos when you unlock those ships.
If you buy a bundle, collection and similar products via the Market, those things will be available to all your ships.
Finally, when you buy a Hero ships, its custom Coating, Pattern, Emblem and Decals will be available to all your ships while its particular custom look will be available to its equivalent Class/Manufacturer.
3 - A Captain Kill indicate that (I think from my experience) you were the one that inflicted the most damage to the ship and thus gains an additional reward to your score of +30.
4 - You will see plenty of new bonus during fights, such as warfare (used a module to kill i think), payback (kill opponent after you're dead) and others.
5 - They have released non-T4 new hero ships. T4 hero ships all cost 4000 G. The Hanuman T3 ship cost 1500 G and the Zilant cost 1000 G. Of course it is because its of a lower tier than T4 that its cost less G.
6 - Currently Officer Briefing are available buring Veteran and Legendary matches. At the start you will have four Officer Briefing all with 101 after their name. There is 16 Officer briefing than can be unlocked in the different technology trees of ships. Check the link below to know which ship unlock what Breifings. However that will change. See second link as well as ship progression.