OBS Studio has the ability to stream to streaming platforms/services such as YouTube/Twitch/Facebook Live. It does have a record function, and you can automatically record streams, but this needs to be enabled in the settings.
What I’m guessing is that you want to share multiple screens/cams via OBS, with your students/school. This is possible, but you will need to create a windowed projection of the OBS output which you would then share via the video-conferencing software.
Zoom did have some issues with Zoom-bombing initially in April, but these concerns were fixed in subsequent updates, which made the platform far more secure. No-one gets into my meetings unless I let them in.
Hope that helps,
Geoff @ TechLeap