1) It's meaning the flotilla that your weapon is firing against. If your ship with Baisc Anti-Gluon Beam at line No.1 is attacking a ship in line No.2, enemy ships at second line will also take damage in form of collateral damage.

2) It's bit opaque but AFAIK, that means the damage bonus for the ship equipping it (in other words, only itself). Targeted CP means the CP of the ship targeted by the ship equipping it (=only itself).

3) One phase lasts 40 seconds and a battle can go through up to 3 phases. Cooldown of typical beam weapon is 6.8 seconds. So beam weapon will fire 18 times in 3-phase-battle. Annihilator beam's damage of single fire can be obtained by multiplying the DPS and 40 (the length of a single phase).

1) mixed up the names "basic"/"extreme" - edited.

2) so be it ... until there is another version.

3) Still can not figure it out. From your explanation we have the time of cooldown. And we do not have the time shot duration. And to calculate the final damage, we will need to multiply the duration of the shot by the number of shots and by the DPS. usually so it is calculated for any weapon. Moreover, having only the recharge time, we still do not calculate the total value, because one shot time of the beam is more than 1 second. And the duration of the Annihilator beam short is longer , than the beam. LAsers and kinetics shots instantly. 

It is logical to assume that this parameter is given as the final calculation of these calculations. Well, unless of course the developers had no intention to confuse the players, because it is sensless to give us only DPS without other data such as cooldown and time of the shot. so I believe that it is just DPS multiply by the time of the battle/phase. 

Otherwise it’s impossible to compare weapons in a game, because other data the game just does not give. Yes, and the time of one phase also does not. But if you do not take into account the opaque description of AB, then you can compare weapons without this indicator. Just DPS vs DPS. 

And if my version is correct, then Extreme Anti-Gluon Beam will deal 36 DPS * 40 sec = 1440 dmg per phase. The question is will this calculation work for AB? Is it 84 * 40sec= 3360? But what bring me here with the question in the first place - the battle animation of the AB obviously shows , that one shot of AB does not last continuously throughout the phase - it is just a litle bit longer than beam. Maybe 5-10 sec. making obvious conclusions from this, we can assume that the calculation of damage for AB is different - DPS 84 * one short per phase max 10 sec = max 840. And 3360 is a big difference to 840. 

On third question, you don't need to handle the duration. Because the DPS displayed ingame is exactly (Damage per shot)/(Cooldown). It is true there is duration of firing but cooldown time in data is comprehensive value on the matter of rate of fire.