Hmm, I've been debating if I should say yes/no before the end of the round. I suppose I might as well.
You're quite right on the 3 guesses.
For the first one, Tetris is good enough for me. I think the song was from the original, but I wouldn't be surprised if they used the same songs in some of the many sequels and spinoffs.
The second is from Zelda 3: A Link to the Past. It's the Castle tune.
Nice how you mentioned FF6/3 for the last one. For those that don't know, the game was released as Final Fantasy 6 in Japan, but as Final Fantasy 3 in the US. (Final Fantasy 4 was released as FF2 in the US). It is indeed Terra's theme, which is played during the intro story sequence. (And just to be clear, this "main" theme is not the title theme, which is different and not very memorable).
Btw, the 3rd song was a bit of a curve ball. I said "well known title" for a reason. I don't know too many people that actually played this game, but pretty much everyone has played a sequel.