One of the primary ways that the Party differs from other dictatorships is that they know full well what they are doing (seeking power for its own sake), so it's perfectly natural that O'Brien would be aware of it. In a sense, the fact that he accepts that is evidence that he's not a thought criminal, and him refusing to accept that would be thoughtcrime.
So, the Party's actual philosophy was a lot different than what it projected to others (big surprise). That being said, O'Brien did, in fact, believe the Party's philosophy - it's just that agreeing with the system means that he agreed with the Party pursuing power for its own sake.
With regards to the telescreen issue, it's worth noting that conversations held while the telescreen was supposedly off were still recorded. (It's not known if that was because the telescreen was on the whole time or if O'Brien was simply using a different recording device).
The book tells us very little about other members of the Inner Party or the specifics of its internal governance structure, so it's a little unclear whether Inner Party members would still be watched by the Thought Police or by other Inner Party members. We do know that the Inner Party is structured as an oligarchy, and that it's very debatable whether Big Brother actually exists or not; these facts at least suggest a relatively flat power structure, but the point isn't directly provable from the books. So, again, it's not clear exactly what the actual mechanism would be to hold another Inner Party member accountable for thought crime would be (especially if there's not actually a central "leader," so to speak).
It's also worth noting that O'Brien insists that the Party declaring something to be true could quite literally make it true; given that he appeared to be truthful about the Party's philosophy in other places, it's safe to assume that he actually believed this himself. This belief is related to - but definitely different than - solipsism. The Party wants to rewrite the past? Well, the past only exists in peoples' memories and in written records, and the Party controls both. The Party says that 2 + 2 = 5? Well, it's true because they claimed it is.
Presumably that belief would entail some kind of doublethink on his part.
So, O'Brien's fully aware of the Party's malice and also believes that the Party can literally control truth. And yes, as @Gaurav pointed out in the comments, "all animals are equal, but some animals are more equal than others."