First off, none of this is intended to be advice and is only meant to point you in the direction of the official sources.
For Australian permanent residency, it will depend on the visa you're after. For example take a look at the official eligibility criteria for the 189 visa
It says on that page that
You must be aged under 45 when we invite you to apply ...
Australia has different visa options for parents wishing to join their citizen children permanently, depending on whether the applicant is in Australia or not at the time of the application.
Outside Australia: there are three possible visas. Two have extremely long waiting times (subclass 103 up to 30 years and subclass 114 up to 50 years), the other a high ...
In Germany, parents of adult residents and/or (EU-)citizens can only be considered for family reunification (Familiennachzug) if you can show they are dependent and need you to take care of them. So I think the answer is: no, having a child who is a resident or citizen doesn't confer any advantage. That's quite typical for European countries.
Yes, you can apply in (most?) areas to enrol in local goverment elections if you are a ratepayer. Often you have to live in Australia as well.
You may have to re-enrol annually, and you will get fined if you enrol ...