I've had that experience (with Cloudflare in general, not DNS). My average response times as measured by Google webmaster tools went from 30ms to 300ms, if I remember correctly. This way ~18 months ago though, so I don't know if it has changed.

And it's to be expected to be slightly slower, at least for dynamic requests, since it's a reverse proxy. I doubt it's limited to the free tier.

I've used the DNS for a few years without any issues whatsoever, so I'd recommend them for that.

As somebody with sites using all three tiers of their service, I haven't noticed a speed difference between any of the tiers.

You can use Cloudflare to manage DNS only, so there is no "slow down".