In the United States, each state's legislature includes the governor of that state, yes.
The Governor submits a state budget to the legislature:)
The Governor and Legislature.
state legislature
You would need the state legislature to impeach your governor.
Appointed
Yes, it is true that in state elections only the governor lieutenant governor and members of the state legislature would be elected under the short ballot system.
It is where the governor lives, where the state legislature meets, and where most state agencies are headquartered.
Yes, each of the 50 states and each of the 5 organized unincorporated territories has its own Governor. The District of Columbia has a Mayor, and the district is under the direct jurisdiction of the federal Congress.
The Governor of the State of Illinois signs bills that the Illinois State Legislature passes into law.
The executive branch (the president).
State legislatures along with the Governor of the state.