This is possible. For email, I now use Fastmail[0]; they've only been getting better these past few years and now even have native mobile apps. The web interface is effecient and very usable! The only things I really miss are (i) undo send and (i) the forgot-your-attachment reminder.

I use Fastmail also for calendar; it supports WebDAV and works very nicely for me on iOS.

For search, yeah, I use DDG as well but find I use !g quite often. Especially for non-English searches. I've heard StartPage[1] is also nice.

I still use Chrome as my main browser, but am looking for alternatives. Besides Safari, I've toyed with Links[2] and Min[3].

For directions, it's still mostly Google Maps although I sometimes use Apple Maps on iOS. I've been explorer Here Maps[4] and have been quite happy with them (especially because you can download entire cities, or even regions, for offline use, including search). For biking, Bike Citizens[5] and Citymapper[6] are also nice (if your city is supported).

I'm sure there are lots of OpenStreetMaps-based services I'm missing.

Edit: If you want to migrate your mail, you can use Google's data download tool[7] to first download everything and then import it into Fastmail or use Fastmail's import tool[8].

0: https://www.fastmail.com/ 1: https://www.startpage.com/ 2: https://links.twibright.com/ 3: https://minbrowser.github.io/min/ 4: https://maps.here.com/ 5: http://www.bikecitizens.net/ 6: https://citymapper.com/ 7: https://www.google.com/settings/takeout 8: https://www.fastmail.com/help/receive/migratemail.html