If not specified, pods are run under a default service account.
An application/deployment can run with a service account other than default by specifying it in the serviceAccountName field of a deployment configuration.
What I service account, or any other user, can do is determined by the roles it is given (bound to) - see roleBindings or clusterRoleBindings; the verbs are per a role's apiGroups and resources under the rules definitions.
The default service account doesn't seem to be given any roles by default. It is possible to grant a role to the default service account as described in #2 here.
According to this, "...In version 1.6+, you can opt out of automounting API credentials for a service account by setting automountServiceAccountToken: false on the service account".
HTH