How to remove this broken latch and handles?
It is definitely the privacy lock that's holding it in place, there's a metal rod that connects the outside, flat head part to the inside knob. If you don't want to re-use the fixture then just saw through it using a hacksaw, dremel or angle grinder (be careful to protect the door from the sparks. If you do want to keep the fixture then you've got to get the screw out using penetrating fluid and a lot of elbow grease. I'd try getting a screwdriver in there and then pounding on it with a hammer to loosen it up and make my own flat head groove, however by the time you're done you may damage it so much you need to replace it anyway.