Your date and time are wrong. Go to Settings > General > Date & Time > Set Automatically (turn ON). The SSL certificates on the App Store will fail if your date is off by more than a few hours.
The App Store will download YouTube version 14.02 or 14.03 (circa 2018). This is a very old version of YouTube. youtube for iphone 4 ios 7.1.2 download
Apple’s iPhone 4 is a compact time capsule: glass-and-steel design, 3.5" display, and iOS 7’s skeuomorphic-to-flat transition. But running apps from today on such an old device can be a challenge — especially YouTube, whose modern app requires much newer iOS versions. Here’s a practical, privacy-respecting walkthrough for enthusiasts who want to revive video streaming on an iPhone 4. Your date and time are wrong