Not sure if you're referencing the petcock or the expansion tank cap, but to open both you'll need to spin both counterclockwise like normal. Sorry if the video wasn't clear.
It should! Check the Yaris and see if the radiator cap lists the coolant as FL-22. That's the mazda specific coolant. Although to be fair, if you completely flushed out the coolant and replaced it with the Toyota red you'd be okay.
