Your missile sensor is exceptional, and that beam fire control is definately capable of being used for antimissile or anti fighter work at Longer ranges than your gauss cannons so no problem there.
Your turrets however only have tracking speed of 12,000 km/s which is limiting, considering your firecontrol is capable of 50,000 km/s, but even that should be sufficient to hit early game fighters.
I need more information about the situation, are you having trouble hitting anything after jumping into a system? Sensors are affected by jump blindness for a short time after transit, also the blindness is far longer you use standard jump instead of squadron jump which is warships.
Are your Active sensors on? Perhaps your fire controls aren't set up correctly, what does the event log say?