You pay the coin cost and get one power for every 6 cards you own, rounded down. It includes all cards.

As for its utility, the deck is okay. Cheap cards that get you low levels of prestige that are meant to be played in combos. But Orgnum patron spammers are some of the easiest players to beat in the game.

Correct. In my opinion, the Orgnum patron should not be taken into account when deciding what deck to pair it with, or to use to counter other patrons. Because the cards are cheap, its pretty easy to get 2-3 Orgnum cards in one turn, depending on RNG and many coins you get per turn. So, while having more cards is "good" for the patron, eliminating cards, like the single coin cards in your hand, so you have a higher chance of combos with the Orgnum cards is better than patron spamming. The odds of your opponent letting your stay on Favored to knock the cost down to 4 are slim to none, so that means you are only going to get 1-2 power for most of the game, while giving up the chance to use another patron or cash out single Gold cards early.

I should have also mentioned that "Contract Action" Treasury cards are not counted in the "total cards" thing, for example Ragpicker or Tithe, but your Gold and Writ of Coin cards are counted.