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Federal Courts exercise fairly limited jurisdiction - they can rule on matters where there is a "federal question" (such as a federal statute involved); diversity jurisdiction (plaintiffs and defendants are from different states) - see: https://www.law.cornell.edu/wex/federal_question_jurisdiction.
If you are deemed a "vexatious litigant" in California State Courts, you cannot avoid this and simply file in Federal Court - you must find a basis to file your suit in Federal Court (federal jurisdiction), or your case will be dismissed on that ground.
A "vexatious litigant" mark does not "bar" you from filing - it only means that prior to filing your complaint you must first petition the court and show that your matter has merit. This is a motion you make to the state court (superior court) to have the court review your claim and decide whether or not it has merit (so that you avoid having another case dismissed immediately - the idea is to avoid having a defendant go to the trouble of responding to a frivolous claim).
This procedure allows even a "vexatious litigant" to bring a valid claim against another defendant.
The statute of limitations on fraud is 3 years from the date that the fraud occurred, or the date that the plaintiff reasonably should have discovered the fraud. (Discovery rule). See: http://www.christian-attorney.net/statute_of_limitations_fraud_misreprentation_california.html for a discussion.
The statute applies in both state and federal court (federal courts apply state substantive laws, but use federal procedure).