The answers to your questions are yes and yes. Assuming you are letting your mount act independently then you may both take actions including making attacks of any type you are able.
You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently. (PH 198)
So you can allow your wolf to act as an independent mount which follows the following rules:
An independent mount retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes. It might flee from combat, rush to attack and devour a badly injured foe, or otherwise act against your wishes. (PH 198)
Being that your mount is using its own actions (not yours) you are able to use your movement and actions as normal. Including, in this case, attacking with a ranged or melee weapon.