There are two separate App Stores: the Mac App Store, apps for Macs and the iTunes App Store, apps for iOS devices.
In the past, you could access the iTunes App Store through the iTunes app for Mac. Apple recently removed the iTunes App Store from the iTunes for Mac app with version 12.7. You now only have access to manage the iTunes App Store on iOS devices through the App Store app on the iOS device.
Or, you can turn to an alternative to iTunes 12.7 and download and install iTunes 12.6.3, which has access to the iTunes App Store on a Mac.
Download version 12/6/3 from this link.
As to passwords on the iPhone, they can be made secure using an encrypted password app such as 1Password. I have used it for years. I do not use the cloud version of 1Password, I use the individual version and sync my Macs & iOS devices with my home wi-fi network only.
ASC - Late 2012 Mac mini, macOS 10.13.3; Watch, 38 mm AL, watchOS 4.2.2; iPad Air 2 & iPhone 7+, iOS 11.2.5; TV 4th Gen, tvOS 10.2.6; Airport Express