Does the gunner also fires missiles against air threats?
Technically, both crew are pilots and either can fly the plane and/or fire weapons. Theoretically, one person could fly and operate the weapons, and it is sometimes done that way.
For example in extremely complex environments where there are friendly ground forces in close proximity with enemy units, or if there are strong threats/jamming in the area of operation, often one crew member will need to dedicate all of his attention on trying to ID targets from friendlies and/or operating the plane's electronic countermeasures or ECCMs to try and spoof missiles and/or burn through jamming while the other guy focuses on flying the plane and engaging any targets his crew mate has cleared for him.
Traditionally, the two crew members split the task between them, with the person sitting in the rear cockpit flying the plane while the Co-pilot Gunner (CPG) sits in the front cockpit and operates the weapons systems. But that is not a set in stone rule, and the two can, or sometimes do, switch roles or take over part of the job of the other when the situation requires it.
For example, when the attack helo is armed with unguided rockets, I would expect the pilot to fire them when performing strafing runs, and the CPG could take over flying the helo if the pilot is incapacitated or spots a target that the PCG hasn't (like a sniper through one window in an apartment block and it would just take too long and the risks too high of hitting the wrong window in trying to explain to the CPG exactly which window to shoot at, better the pilot just take over the weapons systems and take the shot himself) etc.
It takes a great deal of training to get the two crew members to learn how best to operate together seamlessly and to know what each person's role is in different situations, and how best to help his co-pilot.
So, back to your question, when the attack helo is carrying AAMs and hunting enemy air threats, either pilot or CPG can fire the missiles. Depending on the missiles, it is even possible that both pilot and CPG could direct a missile each at two separate targets at the same time if the missile allows cueing from the HMD. The Apache could theoretically have this capability very quickly if the US integrates AIM9X on them. The TY90 will need a much bigger upgrade, or even be replaced with the next gen WVRAAM if the WZ10 wants this capability, so that will involve a lot more work and money.
However, it is unlikely that either designs will be integrated with a HMD+missile combo to allow multiple simultaneous engagement or air threats by both crew, because of the costs required, the small likelihood of attack helos needing such a capability, and also the high likelihood that one of the missiles will be wasted if the two targets split and head in different directions.