if you have a large enough player base to sample, you can determine who is cheating with math. EA Fairplay is pretty good.. Steam's VAC is good, and not some kernel level nonsense..
VAC is so not-good that there are not one but two popular third-party matchmaking services for Valves games whose main selling point is much stronger (read: more invasive) anti-cheat than VAC, and one of them even charges a subscription to play, which highly skilled players gladly pay to get away from the cheaters in high-rank VAC servers.
To some degree, yes. But there are actually many cheaters that intentionally don't play perfectly to avoid detection. That way they appear higher skilled but still within human range.