If a state court rules, for example, that a particular state law is unconstitutional under the state constitution, can this decision be overturned by a federal court?
Federal courts, when sitting in diversity jurisdiction,* are obligated to follow state law as articulated by state courts, as the Supreme Court ruled in Erie Railroad Company v. Tompkins. If there is no controlling state court precedent, the federal court may "guess" how the state supreme court would have ruled, but for particularly important issues of law, it is preferable for the federal court to certify the question to the state supreme court instead.
Under no circumstances may a federal court second-guess a state supreme court's determinations of state law. A federal court may find that a state law conflicts with a federal statute or with the (federal) Constitution, but it may not say, for example, "the state supreme court got the (state) law wrong."
* It is unlikely that a state law would be relevant under any other theory of federal jurisdiction, but 28 USC 1652 does not explicitly limit the doctrine to diversity jurisdiction, so in the implausible scenario where a court not sitting in diversity jurisdiction nevertheless has to apply state law, it must still follow the state law.
Any cause of action advanced at the federal level must have a federal basis, such federal law, the federal constitution, or general legal principles accepted by the federal courts. Simply asserting that a lower court interpreted the state constitution incorrectly is not a federal cause of action. But a state court decision can be challenged in federal court if a federal basis for the challenge can be given. For instance, in Bush v. Gore, Bush argued that the Florida Supreme Court's order of a recount violated the Equal Protection clause of the federal constitution, and so stayed the order.
Also, you ask about a decision "that a particular state law is unconstitutional under the state constitution". This would be especially hard to argue in federal court, as it's likely that the only party with standing would be the state government, and it would rather weird for the state executive branch to ask the federal judicial branch to overrule the state judicial branch. Federal courts are for resolving disputes between individuals and the government, or between governments of different states, not disputes between different branches of the same state government.
A decision that a particular state law is constitutional is more likely to result in a federal basis for appeal, since anyone charged with a crime under the law would have standing. While they wouldn't be able to challenge the finding that the state constitution fails to bar the law in question, there are various other assertions that they would be able to assert. For instance, they could assert that the law violates the federal constitution. If they had originally argued that the state didn't have jurisdiction, and the state Supreme Court found that the state constitution does give jurisdiction, they could argue in federal court against the finding of jurisdiction. Etc.