IANAL, but it seems that many of the above would be heard exclusively in a federal district court, with the exception of some actions based on events occurring on military bases that would be heard in a military tribunal of some kind (i.e., “courts martial”).
For example, DC has its own district court, the United States District Court for the District of Columbia. See 28 USC § 88 (DC is a judicial district). Until recently, it had general jurisdiction just as if it were a state court, applying local law as passed by Congress. Western Urn Mfg. v. American Pipe & Steel Corp, 284 F.2d 279, 281 (DC Cir 1960). Today, the diversity of citizenship jurisdictional statute, 28 USC § 1332(d), defines “states” to include DC; i.e., citizens of DC are akin to citizens of a hypothetical “state” of DC. So the old rule is still the case, but on different statutory footing. Generally speaking, the local federal district court has general jurisdiction over geographical areas that aren’t the part of any state and that are governed by Act of Congress. Further, actions based on conduct occurring on the navigable waters in the U.S. are within the federal courts’ admiralty jurisdiction. 28 USC § 1333. Admiralty jurisdiction is exclusively federal: a lawsuit arising out of a collision on Lake Michigan would be heard in federal court, not an Illinois state court.
But again, there are other sources of federal subject matter jurisdiction that could apply to these cases. For example, controversies over $75K between citizens of different states or an alien and a citizen would get into federal court through 28 USC 1332. Certain kinds of torts – e.g., antitrust torts – would be federal questions since they’re based on federal law (e.g., the Sherman Act), and therefore could get into federal court that way too.
Here’s a funky jurisdictional question: what about actions arising out of conduct occurring on Indian reservations? There’s all sorts of talk of “comity” in the cases in which federal courts dismiss actions so that they can first be heard by tribal courts.
But maybe we should let a lawyer speak up, rather than my Lexis-enhanced WAGs.