Google Alternative?

Would like to get away from Google. I use their search engine, their calendar, have a gmail address, and have a Nexus(google) cell phone. Fairly happy with their products, but dislike supporting companies who hate people like me.

I see lots going to "Duck Duck Go", but what about the gmail account, calendar, etc. Can I use something besides Google and still use their gmail and calendar until I find a suitable alternative? I'm sure the phones would work with anything, though syncing emails, etc might be a problem?