1) In legal writing the two parties' names are replaced by the words "defendant" and "plaintiff." So instead of writing "Mr. Chavez-Kostanopolis" everywhere in a document, they just use the appropriate word. You would not write "the Mr. Chavez-Kostanopolis". OTOH if you want to use the two words as ordinary nouns, then you would write "the defendant" etc. "It sometimes happens that the defendant already knows that the plaintiff is filing suit."

2 "to file suit" view this as a phrasal verb
"to file a suit" view this as an ordinary transitive verb.