there's no cost to google besides the registration fee, if it's your zone, you're paying that fee anyways. The only way to not pay a fee is to go through a free dyndns provider that you have to use a hostname off of their zone.

Is the DNS free, even if you use other registrar than Google?

I have some domains with country-specific tlds, and I'm using small registrars there. he.net is free even in this case.