If I restart my DB, will the database service host env var also be updated? Will restarting a DB or changing the IP of a DB will also imply a restart of all of the services that need access to the DB?
The service's ClusterIP will not change.
Unless you want to also get rid of kube-proxy, in addition to CoreDNS; in that case you don't get ClusterIPs for services.
To be honest kube-proxy and CoreDNS are probably the only components I haven't had problems with on my cluster.
* dnsPolicy: Default
* enableServiceLinks: true (the default)
Then you can use MYDATABASENAME_SERVICE_HOST from the environment and there is no CoreDNS in the path at all.