A republican form of government
Yes and Yes. The US Constitution applies to all the states. Each state has its own constitution that applies to that state. The state cannot contradict anything in the US Constitution, but they can add things that they feel are missing, or have more stringent requirements for certain things. And the state's constitution sets up and defines the government that will rule the state.
Andhra Pradesh
The Constitution.
The 14th Amendment of the US Constitution was significant to the Civil Rights movement in that it stated that no State can produce laws that fail to guarantee equal protection for all US citizens. Thus any law that might impede a person from voting based on race, for example is unconstitutional.
They didn't. The federal constitution came first and then the states. Many of the colonies had royal charters before the revolution.
The Republican Guarantee Clause of U.S. Const., Art. IV:"The United States shall guarantee to every State in this Union a Republican Form of Government, [...]"As a result of this Constitutional value, each State has its own Constitution.
The US Constitution and state constituions
One obligation to the states that the Constitution gave to the national government in Article IV, Section 4 is to protect each state from invasion. Another obligation is to guarantee each state a republican form of government.
the guarantee of equal rights between men and women
In Australia each state and territory has its own set of Constitutional Laws that are legally binding to the original Constitution. Laws can be changed according to the constitution if the High Court can deem the State or Territory law unconstitutional.
A fair one
the Constitution states Section 4. The United States shall guarantee to every state in this union a republican form of government, and shall protect each of them against invasion; and on application of the legislature, or of the executive (when the legislature cannot be convened) against domestic violence.
The structure of each state's legislature is determined by that state's constitution.
establish its own constitution
Each state has 2 Senators, this number is in the Constitution
The structure of each state's legislature is determined by that state's constitution.
Originally the Constitution get each state Legislatures the power to select the senators from each state.