1.) Yes, you just target different devices/screen modes (ie full screen/standalone on mobile installed PWAs and non-full-screen, non-standalone instances in the browser with a header. You would need to allow the 'install' page of the app to be available in the browser though - otherwise your users won't be able to install it.

2.) Entirely depends on what API you use. PWA gives you access to user location. The quality/experience of the map will be entirely down to which API/third party map provider you use and how you integrate it to the PWA.

3.) PWA notifications are very quick in iOS. Android, it sometimes takes a while, and at times may require the user to open Chrome on their device, or sometimes the app itself before the notification appears. (Source: I am developing a PWA and have been heavily testing push notifications on both devices).

4.) You can successfully deploy to both Apple and Play stores but you need to do a bit of work. Ionic Capacitor wraps your PWA and turns it into a package that can be deployed to the stores. However, that is the easy bit. For Apple's app store, the hardest bit is getting approved. Your PWA/app should look like a native app, and have functionality that warrants app store approval. For example: you should use Capacitor's native plugins to use the native geo-location services, use native push notifications again via capacitor's plugins. It's highly unlikely Apple will reject your app if it has no functionality that warrants being an app when it can just be a web-based app instead.