Yes. For non-jailbroken devices, some services offer PC-free downloads, but they are rare. For jailbroken devices, once you have Cydia and Filza installed (which requires a computer to start the process), you can download IPAs directly from Safari on your device and install them via Filza without ever plugging into a PC again.
Using a standard modern App Store on iOS 9.3.5 usually results in a frustrating "This application is incompatible with this iPhone" error. A dedicated IPA library solves several modern preservation issues: ipa library ios 935
The Internet Archive has become the premier destination for legacy iOS software preservation. Yes. For non-jailbroken devices