Jessica is trying to teach some students at home and some in the classroom at the same time. What she's been doing is treating all students as being at home, so they are all logged into Google Meetings. But the problem is, that kids keep forgetting to mute their mics and the feedback is driving her crazy. She would also like to project all the home kids onto the screen so the kids in the classroom can see them.
Leo says that Google Meet has built-in echo cancelation. So make sure that's enabled. Jessica can also mute everyone, but the kids lose the power to unmute if they want to ask/answer a question.
As for casting, Jessica can also Chromecast to a TV set. If the classroom TV supports casting, then she can just press a button and it will cast to the TV. Or she can buy a $40 Chromecast if it doesn't.
There are also mics that can pick up everyone in the room. A shotgun mic would work. They are highly directional. Jessica could also get a mixer and a mic for every kid, but that would be expensive.
Even better, get rid of the feedback by getting headphones like Plantronics and Jabra for everyone and use a headphone amplifier. Then there's no feedback at all.