I'm not sure what you mean by 'intervene'. If you mean, become a party to the case, you would have to have some reason to do so. For example, if two people were suing over ownership of a piece of property and you figure out it's really yours, then you might have grounds to intervene. The court would have to decide if you have standing to do so.
Now, if by 'intervene' you mean submit a friend of the court brief, you have to ask the court for permission, and there may be restrictions, e.g. to ask the U.S Supreme Court for permission to submit a third-party brief you have to be an attorney licensed to practice and a member of the bar of the Supreme Court.
A case over which the federal courts have jurisdiction.
US Court of Federal Claims would hear those cases.
Cases fall under federal jurisdiction if they involve federal laws, the U.S. Constitution, or parties from different states. A case is considered federal if it is heard in a federal court, such as a U.S. District Court or the Supreme Court.
I have seen no documentation that disallows a father from representing any relative in a Federal court case.
Yes, it is possible for a criminal case to be removed to federal court if certain conditions are met, such as if the case involves federal laws or if the defendant requests the removal.
When a plaintiff sues the federal government for monetary damages the Court of Federal Claims hears the case.
Yes
When a case is "removed" to federal court, it was originally filed in State court, but then was "removed" or moved to federal court because it presents some sort of federal law issue. An "answer" is when, in the most common case, a defendant "answers" the claims the plaintiff has made against them.
Depending on the type of court case you can take your case to the appelate court sytem in your state or a federal court of appeals
If you break a federal law (a law that is set by US Statutes and NOT by state statute) your case will be heard in Federal Court.
If the case involves a question of federal law, or if the federal court has diversity jurisdiction (parties reside in different states and minimum amount in dispute.)
A case may be appealed from a state court to the Supreme Court if it involves a federal question or if the state court's decision conflicts with federal law.