Do the federal courts have power to determine jurisdictional issues for state courts?

Answer 1

Only AFTER the state issue has gone entirely through that state's court system and exhausted all state appeals. Even then it must have some applicability or bearing on Federal Law or a Constitutional issue.

Answer 2

Yes and no. Both State and Federal systems have a similar structure, in that each has courts of original jurisdiction (trial courts), intermediate appellate courts, and some form of supreme court or courts (Texas has separate high courts for criminal and civil appeals).

Jurisdiction is established by each system's constitutional and statutory mandates. The United States Constitution and US Code determine what subject matter is heard by the federal judiciary, and by which courts and tribunals within that system; generally, anything falling outside federal jurisdiction belongs to the states or territories. States have exclusive jurisdiction over all cases involving state constitutional and statutory issues (provided the cases don't also involve federal questions, which complicates matters). Occasionally, jurisdiction may overlap, providing plaintiffs with an opportunity for forum shopping or with an extended avenue of appeal.

For example, cases heard under state jurisdiction that also include federal questions (issues of federal or constitutional law), may be appealed from the state judiciary to the federal judiciary once state appeals are exhausted, provided those issues have been preserved (raised at each level of appeal) throughout the state appeals process.

Other considerations that may apply:

• A defendant in a case involving both state and federal or constitutional issues may invoke removal jurisdiction and demand the case be moved from state to federal court.
• Federal courts may exercise supplemental jurisdiction if they hear a case that is substantially within federal subject-matter jurisdiction but also involves questions of state law, such that the federal court may rule on issues of state law.
• Civil cases heard under diversity jurisdiction, where the petitioner and respondent reside in different states must rely on the laws that apply in the state where the case was filed.
• Federal cases can't be removed into state courts.

This is an incomplete overview of a very complex subject. Law schools offer entire courses related to the powers and limitations of state and federal courts.