Suppose I live in State A, but am on vacation to State B. While on
vacation, suppose someone living in State C, but currently in State D,
accesses my bank account to take money out illegally. The bank has a
central headquarters in State E, although my branch of the bank is in
State F.
In which of these states could I file a lawsuit? Any of them? All of
them?
The thief would be the defendant in a lawsuit brought by you. The fact that you are on vacation in State B is irrelevant.
You can always sue someone where they are domiciled, so State C is one forum where you could sue the thief. You can also always sue a natural person (as opposed to an entity) in a State where they are physically served with process, so if a summons from the courts of State D were served upon the thief while the thief was in State D, then State D could handle the case.
You could also probably sue in State A on the grounds that intangible property is deemed to be located where the owner is domiciled and the theft of intangible property was a harm directed a State A. But, there is an argument that if the thief has no way you knowing that you lived in State A as opposed to State F where your branch is locate, that the thief's actions were targeted at State F. State E would not be a very plausible state to argue that there is jurisdiction.
A federal district court has geographic jurisdiction only over cases that could be heard in the state courts of the state where it is located, so a federal court case would be brought only in the states where a state lawsuit could be brought. A federal court cases would either have to seek at least $75,000 (since there is diversity of citizenship between you and the thief), or would have to state at least one theory arising under federal law (which might or might not apply to this case).
The you can choose which state to file in from those that are available.
Which of these states could file charges against the person?
A state can prosecute if the crime happened there, or if the crime caused a harm there. In this case the answer to both of those questions could be muddy. Basically, State A or F is probably where the crime caused harm, and it isn't clear from the OP facts where the crime was committed by the thief (we only know where the thief is now).
These acts would also probably violate some federal crime that could be prosecuted in federal court, mostly likely the federal courts in State A or State F.
Which of these states could file charges against the person? Could the
federal government file charges as well? Would more than one
prosecution violate the double jeopardy clause of the Fifth Amendment?
What if these were countries instead of states?
The double jeopardy clause applies to prosecutions within a single U.S. state, and in addition to any state prosecutions, a single prosecution can be made at the federal level. Likewise, prosecutions in different countries do not count against each other for purposes of a double jeopardy clause.
Many U.S. states have a binding or non-binding policy of not prosecuting crimes that have already been prosecuted by another U.S. state or by the federal government, the U.S. Justice Department likewise has a non-binding policy of not prosecuting cases which have already been prosecuted by a U.S. state or another country. But these policies do not have constitutional dimensions and are not required by the 5th Amendment.
if I use a Canadian Wi-Fi network without authorization from within
the United States, would US or Canadian law apply?
In criminal cases, choice of law and jurisdiction over the case are the same thing, because a state or country can only apply its own criminal laws.
In civil cases, choice of law is a question distinct from jurisdiction. A court applies the law with the most significant connection to the disputed legal issue in question (sometimes more than one set of laws in a multi-issue case), even if it is the law of a different state or country, which is a standard that affords a judge considerable discretion. Either U.S. law or Canadian law could be plausible to apply in this case depending on the detailed circumstances and the legal issue that is disputed.