You can take on more risk and not get any more return. Conversely, you can get more return and not take on anymore risk. That's like the foundation of Modern Portfolio Theory.
Theory tells us that you can't get more return without taking on more risk, if the market is efficient.
Of course, the market can't be perfectly efficient, but it's possible that the market is weakly efficient: the cost of information is so high that it, on average, makes it impossible to beat the market.
No, only if the portfolio is on the efficient frontier. There are many sub-optimal portfolios that do not have the best return/risk trade-off, like portfolios with a lot of specific risk. Check out the Markowitz Bullet.
Specific risk does not get compensated because it is easy to eliminate it with diversification.
I should have been more specific (no pun intended). You should take a closer read of my comment. You've made the same misinterpretation a second time.
Suppose a non-diversified investor, A, owns an asset which has both systemic risk and specific risk, and a diversified investor, B, has the same knowledge as A. In this case, B would be willing to pay a higher price for the asset than A would. A then sells the asset to B and the market becomes efficient. No assets would exist not on the efficient frontier.
