does iPhone connected to MacBook use power from usb or its own battery?
The iPhone always draws its power from its own battery. However, when connected by USB to a MacBook Pro, it will at the same time charge the battery. So depending on your use-case, it is commonly possible to run the iPhone indefinitely in this mode. Remember to power the MacBook Pro from its charger, and ensure that the MacBook Pro is not so heavily taxed that it actually uses more power than the charger supplies.
When using Zoom on an iPhone, any storage used would be on the iPhone itself - not on an USB-connected MacBook Pro. However, streaming a Zoom class doesn't really use up any storage worthwhile mentioning - unless you're recording it.