On the topic of fairness, I have been tracking my hole cards over the past 45,000 hands. The odds of being dealt pocket aces are 1-in-221 or about 0.452% of the time. Across 45,000 hands, I have been dealt AA about 0.486% of time. So it seems like the shuffling algorithm is fair to me, and I have no reason to believe that the board is unfair either, since those aces rarely got cracked. Of the times I was dealt AA, I won 90% of the time, which is above expectations.
On the topic of how to recognize a strong player, a reliable indicator is that they take control of the action. If you watch the top bankrolled players face off, you will notice the almost complete absence of limping in, which is the opposite of how most people on this site play.