Most IR seekers use liquid nitrogen or similar to cool the missile seeker head, to increase the sensitivity. I think the nitrogen is pumped through a connector on the launch rail from the plane.
Obviously this connction is broken when the missile is fired, but with the rather short life time of the seeker once the missile is fired, I doubt the sensitivity of the IR sensor will decrease much.
The missile seeker can be steered onto the target before launch and locked on. This can be achieved by slewing the seeker, using the radar to point it at the target, or by using the seeker itself to scan for targets (Uncaging the missile), where the IR sensor scans across its field of view looking for a hot target.
IR missiles can also be fired in Boresight mode, where the missile does not lock onto a target until After it has been launched, locking onto anything that flies through it's field of view. I don't know whether any missiles use radio IFF recognition to interrogate targets, so firing a missile into a furball in Boresight mode might get a friendly killed.