You can't even install the resulting binaries of an opensource Android build on a phone because of gaps. And even if you could (or fill in the gaps) Google poisoned the ecosystem by ensuring almost all Android apps require Google Play services. Which aren't open source and you realistically need for all Android apps.

So no, Google made sure there is no open source Android. There are just some (incomplete) source dumps.

It sure is. Open source doesn't require open development model or even taking outside contributions. It simply requires that you have access to the source and can do things like fork it, which you absolutely can with Android. I think people android to be more like Linux, but that's a very difficult arrangement and has tradeoffs.