Is a consulate in its own sovereign state?

Question

I know embassies are considered part of their respective country, but is it the same with consulates? And is the physical earth part of the sovereign state, or is it just the people in that area?

Answer 1

Sorry. Embassies are not "part of their respective" countries. Neither are consulates. Diplomatic properties are only protected under the Vienna Convention on Diplomatic Relations, which is an international treaty the privileges and immunities of diplomatic missions. Read about it here:
http://www.un.int/usa/host_dip.htm

Regarding your second question, sovereign states are defined by their territorial limits, not the locations of their populations.