Does Dual Laser Turret on a Gozanti give it 360 firing arc or is it limited to the front half with a 180 firing arc as it would be limited to the blue line? I searched the here but didnt find anything that specified

Its the same as any other turret.

Turrets do not have a 360 arc, they may fire out of arc but if they do then various "in arc" effects do not work and "out of arc" effects do work (Tactician or Autothrustors respectively as an example)

For the most part, ignore the printed arc when firing with it. If something on either your ship or your target has an arc-specific effect, then you need to pay attention to it.

edit: totally missed the question....

The blue line restriction only appears in the section describing Turret Primary Weapons, so I think the Dual Laser Turret gets by. It helps that on a single card ship like the Gozanti, there's no obvious reason to pick one base over the other as the "source" of the attack, for purposes of drawing the line that checks for blue line obstruction.

The confusing thing is what the card says and then there is the blue line for epic ships where the front arcs cant fire behind it and the aft arcs cant fire in front of it but the Gozanti has only one section , no aft and fore. So does this mean that there is no "Blind spot" and it can fire front and back, only front in a 180 arc or do I choose what section it fires from?

The card says :

GOZANTI-CLASS CRUISER ONLY.

Attack (Energy): Spend 1 energy from this card to perform this attack against 1 ship (even a ship outside of your firing arc).

The only weapon that is called out as having to respect the blue line is a huge ship's Turret Primary Weapon. Ignore the blue line when attacking with a hardpoint turret.