No.
Dispatchers have the ability to multi-select, or patch, talkgroups together, and could effectively go citywide by doing so, but there is no (unencrypted at least) dedicated citywide talkgroup.
Not specifically. They use PSAP East and West to talk to other agency dispatchers. When one checks "citywide" for a resource, the precinct dispatcher uses an instant messaging service on the dispatch console that all the other precinct dispatchers are on (think group texting). This keeps it within the agency, and is typically not voiced over the air. The individual precinct dispatchers will then ask on their respective talkgroups, so the originating request dispatcher doesn't have to switch off of their talkgroups.
Ah for the days when Phx was still on VHF and you heard all hot traffic on Chase and the Chase Dispatcher would occasionally do other citywide boradcasts.