If I create a new wizard under my member account, will that new wizard have membership too? Or will my first wizard be the only one who has membership?
Your Wizard101 account EpicViperfalcon is currently a full Member. Any Wizards you create on that account login will benefit from the Membership perks.
If you create another account and add it to your Family of Accounts, it will need its own Membership.
However, much like reading a chapter book, Wizard101 is sequential game play (before you move to level 2 you must complete level 1). Even if you have purchased a Membership you must first complete all of the quests in one world to be able to move on to the next.
The same thing goes for Access to some of the streets or areas within a world. For instance, when you've successfully completed the quests for Wizard City you will be given a quest to enter into the next world, Krokotopia. Once you have your own access there, as long as you have a Membership or have purchased the Premium area with Crowns, you will be able to enter that world freely.
Each Wizard on your account must earn their own way through the Spiral, but as long as your Membership is active, you will not be required to purchase individual areas as you progress.