Does each state government have its own legislative and judiciary branches?

Question

I'm absolutely TERRIBLE with politics and government. In fact, I don't even know whether I'm democrat or republican. If someone could please answer these next few questions for me, you'd be my lifesaver...
1)Does each state government have its own legislative and judiciary branches?
2)Define federalism (on a low enough level that someone who knows nothing about politics can understand it).
3)Define Republicanism (same applies here as above).

Thank you soooooooooooooooooooo much!!!

Answer 1

Each state has its own executive, legislative and judicial branches because Article 4, Section 4 of the U.S. Constitution guarantees each state a republican form of government.
Federalism is a system of government where the States cede certain enumerated powers to a central government and keep all other powers to themselves in a delicate sharing of power.
Republicanism describes a system of government where there is no monarch as head of state.

Answer 2

1. Yes, each state has its own legislative and judiciary branches. For example, the state of New Jersey (just an example) has its own Senate and Assembly, and also its own state Supreme Court, which fall into the legislative and judicial branches, respectively.

2. Federalism, in general is when a national government and individual state governments work together. The national, or federal government, is given certain powers, while states hold other powers not given to the federal government.

3. Republicanism is basically a form of government in which the people are represented in the government. Through direct democracy (voting) and participatory democracy (electing representatives) the general public is represented in government and may influence the government through the rights the people are given.