Yes, the App Store is certainly supported on the iPhone 5S.
Note that the iPhone 5S does not supported the just released iOS 13 release. This means that apps that require iOS 13 or later won't be installable on the iPhone 5S. For the moment, only very few apps require iOS 13.
If an app does require iOS 13, and is not available for download, usually the ...
You can't disable one app update access.
You can turn off automatic updates and not update it manually, to turn off automatic updates:
Go to Settings
iTunes & App Store
Find App Updates and turn it off
You just need to delete the app (or, more specifically, the icon placeholder for the app) from your iPhone's Home screen. Then when you go to the App Store again you should get the cloud download symbol indicating you've previously purchased the app. Tap on that and it should download just fine.
To delete apps from the Home Screen on iOS 13, follow these ...
I don't think there's a specific way to know. I have the promo $100, too, and I was looking into this.
The only way I found out was to check on the available balance every few weeks. Even doing that, you have to accept that you might go over the promo amount. Of course, this is exactly what Apple is hoping will happen (in my personal opinion; I don't ...
The steps you describe are correct, yes. There's however no need to do it manually like you describe - you can just choose Distribute in Xcode to automatically send your archived build to Apple. Just like you would if the app was going on the App Store.
The difference between putting the app on the App Store, and doing what you want, is simply this one step:...
These instructions are for iOS 13. It should be the same for versions going forward in the immediate future.
Open the Wallet app.
Tap your Apple Card.
Tap the ••• button in the upper-right corner.
Scroll down and tap Make Default at Apple.
These steps make your Apple Card the default payment method for all of your transactions with Apple, ...