The whole city has NOT been evacuated, they evacuated several blocks, and have set up an exclusion zone, which encompasses the area around Martin Place from Hunter St down to the top of Hyde Park. It is not anywhere near as large as the CBD. In fact, police and the government have said if people have plans in the city that don't involve going into the exclusion zone, they should still feel free to go out. Trains are all still running as normal, except they are not stopping at Martin Place Station, which is in the exclusion zone. They are, however, still running under it.
There is apparently an authentic list of demands, but it has not been reported by the media, because the police have explicitly asked them not to disseminate that information. There have been many posts on social media about what the demands are (many of them conflicting), but we simply don't know. Anything else is pure speculation.
For what it's worth, I suspect this guy envisages himself as part of a wider jihadi movement, but is probably a lone wolf. There hasn't been any solid confirmation of a bomb threat - if there was, I suspect police would be widening the exclusion area and would be discouraging citybound travel, rather than encouraging it.
The US Consulate is, I believe, within spitting distance of the cafe, which would be why they've evacuated it. They've basically been trying all day to clear the area and stop people from being within eyeshot of the cafe.