These challengers to Google are increasingly adopted, especially in Europe. This blog article by ExpressVPN gives a list of the most up-and-coming.
Yes, an important trend. I’ve been using DuckDuckGo excusively the last year and only very sporadically fall back to Google (mostly for image search, filtered by public domain license).
Besides directly using search engines there are also a number of so-called Meta Search Enginges. These provide an extra layer above the actual search engine queries and invoke searches to multiple engines, aggregating the results.
They can sometimes provide additional privacy features. I recently added one such engine - a FOSS project - to awesome-humane-tech list. It is called SearX and allows you to host the engine on your own server.