Is it possible to power Google Chromecast or similar via the Mini USB port?
It appears the Mini USB port on the W77OST is not powered and meant for service use only. (see http://support.benq.us/customer/portal/questions/12253631-what-is-the-type-mini-b-usb-on-the-mh63-used-for-)
Other projectors have a power management menu where this very port can be turned on an off. Is that possible with this projector?
Unfortunately no, that port is for service only and does not have a way of providing power. The chromecast would need to be powered separately.