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That a state had the right to ignore a law, if it thought the law was unconstitutional
If a state court declares a state law unconstitutional, the state will probably appeal the case to the state supreme court. If a state court declares a federal law unconstitutional, the losing party in the case will appeal the decision in the federal courts. The case could ultimately be heard by the US Supreme Court; however, if a lower court reverses the state court's decision and either the appropriate US Court of Appeals Circuit Court or US Supreme Court decline to consider the case, the decision of the lower federal court would be final. The US Supreme Court is the ultimate arbiter of constitutionality.
That a state had the right to ignore a law, if it thought the law was unconstitutional
Any state or federal law, executive order or treaty that's relevant to a case under review in a court and operates contrary to the Constitution.
The case was important because it was the first time the US Supreme Court found a state law unconstitutional. This case was in 1810.
I am not sure what you mean by "act." There is no one act that applies here, but there is a procedure for determining whether a law is unconstitutional. It usually involves a challenge at the state level first. After that, the case is then taken to a district or federal court, and finally, it is taken up at the Supreme Court (assuming the Supreme Court decides to take the case; they do not take every case they are asked to review). But under our system of checks and balances, while a state's attorney general or an individual plaintiff from a state may challenge the constitutionality of a law (such as President Obama's health care law, or the Defense of Marriage Act), it is the Supreme Court that has the final say on whether a particular law is unconstitutional.
No. Statutory law will always take priority over case law. Case law is made when the given statutory law is either unconstitutional under the applicable state or federal constitution, vague, contradictory, or silent on a particular issue. But sometimes case law will be codified into statute by the appropriate legislative body in question.
Nullification
When the law is deemed unconstitutional.
The Supreme Court declare state law unconstitutional
If there is written law in that country that lead to that,yes
It allowed the Supreme Court to overrule an unconstitutional law.