I have the pj660 n it can connect via a cable but you need to get from Sony. About $50 iirc. Anyway, the projector is for fun n the lumen depends on their model.
Saw in Sony showroom. Told the sales staff this may be a gimmick. The lamp is not too powerful and it cannot project far.
You may need to dim the room. It drains the battery fast. If high lumens then may get hot.
Anyway, it was meant to be a selling point. A way to differentiate Sony from other brands.
I think it has microHDMI port.
HDMI is not the video file format. It is just a compact audio/video interface standard for cables and ports.
The videocam probably records in MPEG4 format.
You would be able to port any MPEG4 video from mobile phone or tablet or PC to the videocam and project it.
Got once, I saw the wall on the bed room dark enough for me to project the video of panda. quite ok if not fussy about it. But must mount on tripod else hand tired. Ha ha!