Can somebody explain to me the engage phase with Omega Squadron Expert and Quickdraw on TIE/SF ship with Special Forces Gunner ( turret rotated backwards ). Do they get to shoot double in the front arc or they can shoot either side ? When Quickdraw lose his shield does he get another bonus primary attack ,which makes him to shoot four times per round ?

Do they get to shoot double in the front arc or they can shoot either side?

They get an extra die if the is in the , then the ship gets an extra die during a primary attack. If the is in the the , then they may make 1 primary attack and 1 primary bonus attack. Special Forces Gunner does not grant 2 attacks in the same arc.

When Quickdraw lose his shield does he get another bonus primary attack ,which makes him to shoot four times per round ?

A ship may make only 1 bonus attack per round, so Quickdraw is still limited to only 1 bonus attack from his ability or from Special Forces Gunner but not both.

There's a lot to unpack here, so let's go one at a time.

1. Every TIE/sf Fighter has a mobile arc that can only ever aim forwards or backwards. To simplify matters, that means you can never shoot sideways with a TIE/sf.
2. With Special Forces Gunner , depending on where the mobile arc is pointed, you have some various options:
   1. If the arc is forward , then your primary attacks out the front are at +1 attack die. That means 3 dice at range 2-3, 4 dice at range 1.
   2. If the arc is backward , then your primary attacks have no inherent bonus, but after you perform a primary front attack, you can perform a bonus primary turret attack (backwards).
   3. If you have any missiles defined as front arc attacks, then those missiles instead are turret arc attacks.
3. Quickdraw gets to perform one bonus primary attack, any time after losing a shield (this could happen outside the engagement phase, due to a variety of effects). Importantly, though, a ship may only ever perform one bonus attack per round! That means Quickdraw can:
   1. Shoot forward when he engages, then perform a bonus back attack.
   2. Shoot forward or backward when he engages, and separately, perform a bonus "revenge" attack.

Remember, a ship can never attack more than twice in a given round: once when it engages, and once when granted a "bonus attack."

It's worth noting that, back in First Edition, Quickdraw could indeed perform four attacks in a single round, if he were positioned perfectly. That's what made him so deadly in that version... now, not QUITE so much.