I never really use the camera for anything meaningful, and prefer video call on the laptop.

Don’t think projector phones exist, just a wishlist for something cool!

Max 4 inch screen, IR blaster, physical keyboard with speed dial settings for buttons, form factor like the Xperia x10 mini pro, headphone jack, cameraless, LED with customisable lights for different notifications, bonus - built in projector, satellite phone capability,