iOS 7 is awful compared to iOS 5 or iOS 6. My commiserations. I regret having upgraded.
I don't use Apple's ugly and lame default apps like Calendar and Safari. However, there is in-page search in iOS 7 Safari, too. They just put it somewhere else. (A Safari user might assist you.) I prefer using browsers like Atomic Web Browser, Mercury, Dolphin, and for calendars, Calendars 5.
There is definitely a new native YouTube app for iOS 7 directly from Google. Just make another App Store search. It has a totally different icon compared to iOS 5 -- now a red field with a white "play button" symbol. It's a low-quality, unwieldy app, but it's the official one from Google. Well, the YouTube app on iOS 5 was similarly low-quality and unwieldy. I hate there are no multi-touch gestures for forwarding/rewinding 5 or 30 seconds, etc. etc. That should be elementary functionality in a video app. As it is, it's just a crude app, but Google is apparently happy with providing crude, unsophisticated functionality.
