Yes, all web applications can be accessible from the internet with FBA.
If you don't want the users shared across web applications then you will need a separate membership provider setup for each web app. You can reuse the same database for each one if you like, by giving each membership config a different "applicationName"
setting (Or just create a seperate db for each membership provider setup).
You can manage all FBA users through the FBA Pack. It includes a user management page that allows you to create users, edit user details and permissions and reset passwords. Some screenshots are here: