Google may be able to control the Element app on the play store, but at least for the server side there's no way to do that with synapse (the official matrix protocol server side implementation), which is fully open source and distributed directly from the developers.
Yes, but IMO the Matrix team should _really_ focus on Dendrite since Synapse is extremely resource hungry and prevents a lot of people (including me) from running their own servers.
It's not that resource hungry anymore. Hovering stably around 500M RSS and 8% CPU for me right now. That's with ~25 users and a lot of federated, public rooms, some of them quite large.