Except now you presume we're ONLY talking about SETI, which is quite wrong. ANY of our astronomical observations should be able to pick-up signs of advanced life... Think, artificial light, Dyson Spheres, planetary engineering, etc.
I don't see why. Well, Dyson spheres would probably be visible, but everything else is negligible compared to the power of a star.
No, to me, the biggest part of Fermi's Paradox is: why don't we see the aliens on our own planet? If aliens are so likely, there's bound to be thousands of civilizations that are millions or billions of years ahead of us. Even if it takes thousands of years to colonize a single planet, they've had more than enough time to colonize the entire galaxy several times over. Shouldn't we at least be finding their robotic probes in orbit around our sun?
But if jythie is correct that the sun is an unusually old Population I star, then that makes it more likely that we're one of the first, and nobody got a billion year head start on us.