Is this the company that supplies/makes the puller for Hornady?
Yes. They make the RCBS model as well. Believe they're out of San Antonio, Texas. All the companies outsource somewhat.
Also, the rubber o-ring that surrounds the collet is cracked or cut in one place between the three separate parts. Or is the O-ring supposed to be in one piece?
Supposed to be in one piece. Have then send you another or buy a local replacement, they're cheap. Or better still, use a shell holder from your press instead.