Now, to address your second issue, conflicts between state laws and the federal constitution.
Early on in the history of the Supreme Court of the United States, it was decided that the Court had the power to review whether or not state laws were incompatible with the Constitution, or with federal law, and, if so, said laws became unenforceable. The main case is Martin v. Hunter’s Lessee, 14 U.S. (1 Wheat.) 304 (1816). In it, Justice Story established (Chief Justice John Marshall was unable to participate as he had a personal interest in the outcome of the case) that the Supremacy clause of Article VI of the Constitution, combined with the grant of jurisdiction under Article III to the Supreme Court over all cases regarding federal law and the constitution, meant that the court was the proper body for deciding whether or not states, through the laws they had made, had overstepped their limitations on sovreignity. This is not an explicit statement in the Constitution, but, like the decision in Marbury v. Madison, which arrogated to the Supreme Court the power to declare acts of Congress unconstitutional, was assumed to exist in order to carry out the apparent intent of the Constitution, as it had been written. In short, someone’s got to resolve such issues, and the Supreme Court appeared to be the best bet.
So, let’s say a state passes a law. For kicks and giggles, we’ll say that Ohio passed a law which prohibited anyone from importing wine from California, ostensibly because of health issues, but in reality because it is so much better than the wine produced in the Lake Erie district, severely limiting sales of Ohio wine (side note: do not EVER bother to drink Lake Erie wineries’ products). There being a number of people in Ohio who love California wine, one of them files a lawsuit in federal District Court, requesting a writ of mandamus, ordering the state of Ohio to allow the importation of California wine, on the grounds that the statute passed by Ohio is in conflict with the Constitution’s provision that Congress gets to regulate interstate commerce, and has done so with regard to wine.
The matter proceeds to hearing, with both sides (the plaintiff, John Doe, let’s say, and the defendant State of Ohio, which simplifies things; don’t ask… ) offering both briefs of case law and oral arguments to the judge. The judge decides that Congress hasn’t regulated this particular area of interstate commerce, so Ohio is free to do so, and dismisses the petition. Plaintiff appeals, to the 6th Circuit Court of Appeals. After briefing and oral arguments, the 6th Circuit panel hearing the case overturns the decision of the judge, declaring that the Supreme Court has specifically stated in the past that a law which mentions an area of interstate regulation in passing, while talking about anything having to do with alchohol, has as a result prohibited the states from interfering with their own laws on the subject (this is a made up precedent, for the purpose of this hypothetical). They issue an order to the judge to grant the petition and issue the writ requested by the plaintiff.
Ohio is not happy, so it petitions the Supreme Court of the United States for a Writ of Certiorari (meaning it requests that the Supreme Court hear its appeal of the decision at the 6th Circuit - not something the Court is mandated to do under the law, but up to its discretion). Cert is granted, the Court feeling that the issue is very important, or perhaps because just last month the 4th Circuit reached the opposite opinion regarding Virginia’s attempt to do the same thing. Again, briefs are filed, arguments heard, and the decision of the Court is issued. The Court, based on its past decisions, and the facts and issues in the instant case, decides that Ohio cannot bar California wine for health reasons. The law is declared unconstitutional, the case is returned to the District Court with instructions to issue the writ as requested.
Now, you ask, what happens to Ohio Revised Statues §41.666, the wine-banning law? Well, it sits there in the books unless and until someone comes along and removes it. BUT, it will never be enforced, because it has been declared unconstitutional. Whenever someone looks up the statute, they will usually be informed (depending upon the method they use to look it up) that it has been declared unconstitutional. Possibly, at some future date, should Ohio’s legislature undertake a recodification of its laws, they might remove the statute from the books, but it otherwise has no effect.