Here are some Synonyms for all of the words:
Court reporter: steno-type reporter, stenographer, and brachygrapher.
Criminal Case: there are no synonyms for criminal case but, there are some for criminal: criminates, criminalities and coming close.
Cross-Examination: analysis, search, survey, question, investigation and inspection.
Defendant: suspect, litigant, offender and prisoner.
Direct Examination: there are no synonyms for direct examination.
District Court of Appeals Federalism: there aren't any synonyms for this word so I'll just give you the synonym for the big words in the sentence.
District: region, neighborhood, section, territory and community,
Court: street, plaza, enclosure and patio.
Appeals: claim, demand, call, suit, bid, question, address and proposal.
Federalism: unionism, Unitarianism and republicanism.
I'll do the same thing for Florida Circuit Courts that I did for the one on top of it.
Florida: there's no synonyms for Florida.
Circuit: course, district, lap, route and tour.
The synonyms for Court are already up there.
Hope this answers your question :)