Can I get notifications on MacBook Air without keeping apps open?

That’s generally the way it works. An app would need an always-running background component to post notifications if the app itself isn’t running. Another option is push notifications, but that depends on the entity hosting the service to provide them.

How about if you just Hide the Apps instead of quitting?

imkhan5251 wrote:

How would I set up a background component for these apps?

You don't. The developers of those apps would have to configure them to work that way.

This looks like you want to Port Over the functionality from an iPhone running iOS onto macOS

Although both operating systems are built by Apple, the functionalities work differently.

You can have an application Open and Loaded into Memory (RAM ) , though minimized into the dock, as suggested by the previous Contributor @BDAqua

In which case, the Notifications, if properly configured, should be presented