Of course you can. If you invented it, and nobody else has patented it, you can patent it. Opening the source doesn’t invalidate your rights as an inventor or copyright holder, though it can add confusion and/or complexity to the enforcement of both the patent and the open source license.

Yes, but my understanding is that publically detailing how your invention works _before_ trying to patent it means the invention becomes public knowledge/prior art. That is, so long as you submit a patent application before releasing the open-source code, it should be OK, but there's no much you can do once the cat is out of the bag.

I imagine the rules and best practices would vary between jurisdictions, but basically yeah. But as soon as you file for the patent, you can release source and enjoy the confusion.

(Based on 30 seconds of googling, it seems that the USA and Australia gives inventors a 1 year grace period after publishing, but the granted patent might not be valid in other countries.)

USA also used to not consider publications or patents published outside USA as prior art, to the point of granting patents that were rewritten from someone else's patent in another country.

Not sure if it got better or worse with WTO patent rules.

Considering the history of NAND flash amounts to Toshiba applying to Japan's patent office and getting laughed out of the room, then Sandisk saw it and applied for and received a patent for NAND flash from the US Patent Office, it's probably still the case.

Arguably patents as intended should require description of patented device/technique in detail that allows replicating it - effectively open sourcing it.

The patent then serves as temporary moat on applying that specific technique or producing that specific device to refund the inventor.

In practice... well, sometimes patents were used to recover details of closed-source software or hardware.