It depends on how you set Safari in ios. You can choose between google, yahoo and bing. Any searches done on safari will follow search engine that you set.

Now if you use the search window in iOS, the phone will search links within apps too. The answer will be categorised in groups such as websites, web searches, siri base etc etc

If you want to search a location in wave for example, then open waze app and search.

http://flip.it/p3yXRA
This is from 9 to 5, Apple has unintentionally or otherwise open their server to downgrade your iOS 11. Check it out if you are interested.

Seems the battery level does affect the standby drain?

Yeah, I believe this is the case. It'll drop much lesser or not at all when at 100%.