Could my team be ranked in the top ten in the US or Korea or wherever if we only ever play via the internet?
Very high. You can see for yourself here[1]. Anecdotally, I had a player on my team that cheated in an (online) semi-final match. We had no idea, but were moved down a league, were disgraced, and obviously cut him. A year later, he was one of the people that toured the country with the XFX team. I couldn't believe it. Every one knew this guy cheated just a few months prior, now he was offered a contract. I was very active in the Socal LAN scene, and know at least 3-4 players that played professionally and cheated.
As far as your second point is concerned, some aimbots are so tricky, even local human observers couldn't catch them. I saw this proof of concept made by a famous cheat maker where the mouse would "tug" at the direcction of the player through a wall. The movie would be almost imperceptible by a spectator, but definitely "felt" by the player.
[1] https://www.hltv.org/blog/13538/cheating-on-professional-lev...
Well the answer is surprisingly simple. Suppose you only have one person that's wallhacking on your team. He's calling out positions for everyone else. He can play terribly, but since the calls are going out, your team still wins. (This is not a hypothetical and has actually happened in high level matches before.)