I don’t believe log parsing is within the scope of official support, so you probably won’t find much help with it here. That said…
See what the HERO_ENTITY tag on your player entity is set to after the mulligan. Then go find the card ID of that entity.
If you’re looking for what cards became a triple, I think there’s an entity that watches for the moment you grab the third card - TB_BaconShop_3ofKindChecke. Look for triggers by that which generate new entities.
The tag for a player’s placement in the current game is PLAYER_LEADERBOARD_PLACE. I don’t believe the Power log contains any data regarding the matchmaking ranking though.
You may find a community like the Hearthsim Development Discord suited to questions like these, at least at times when someone’s around to help. That last question actually came up there a week ago. https://discord.gg/hearthsim-devs