No one ever really uses "I came to know" in every day conversations. I don't remember hearing anyone say that. It's more something you might read in books. It's not necessary to say "I came to know" before "he had already finished it". But you could say, "I found out he had already finished it," or "I saw that he already finished it," but it's really not needed. The meaning is implied. "Before I played video games, I had finished my work," is grammatically correct, but no one would really put it that way. You could simply say, "Before I played video games, I finished my work," or "I finished my work before playing video games." Hope this is helpful. :)

When I went to my friend's house to help him complete his project <- Past Indefinite he had already finished it. <- Past Perfect action before action in the past Before i played video games,i had finished my work. <- correct