This company (会社) has done the ritual required to create stocks for their company. When a company has stocks, they become a corporation.
The readings for everything here are the readings you learned with the individual kanji, though not all are on'yomi. This word is usually rendaku'd too, but sometimes you'll see the non-rendaku version when it comes to English language legal stuff, so keep that in mind.
Can you call Tofugu Corporation to make sure the fax went through alright?