Engine experiencing misfire after a rough start.

[KARlosfuentes]

I am inquiring for a Ceed 1.6 petrol car with an 08 registration. If I have difficulty initiating the car's ignition, requiring a second attempt to start it, the vehicle consistently has misfires throughout operation. However, this is not always the case. The engine often starts on the first attempt and operates without any issues, exhibiting a seamless performance. This issue occurs around four times every week.

[STAR89colin]

Examine the coolant temperature sensor, coil packs, and plugs. The coolant temperature sensor regulates fuel supply during engine start-up. Malfunctioning sparks and coils, together with improper fuelling, result in harsh engine performance.

[KARlosfuentes]

I replaced the spark plugs in November when the issue first arose. I have not replaced the coils since acquiring the vehicle, and it has already accumulated a mileage of 185,000. I believed that if there were coils involved, it would be shown as an ignition malfunction on the dashboard. Is replacing the coolant temperature sensor a straightforward task?

[KARlosfuentes]

This is the sound produced by the starter. The noise persists even after replacing the starting motor.
I will inspect the spark plug gap, since I recently inserted them without verifying the gap. What should be the appropriate magnitude of the gap?