We can't travel at light speed if we've got any amount of mass. Photons have no mass whatsoever and they don't experience time the way we do. Now that that's been cleared up, yes I think we'll be spacefaring within 500 years. I hope it's something like Halo though with all the beautiful planets and the spectacular vehicles and weaponry and even the AIs like Cortana. Oh what I'd do for a trip to Beta Gabriel or Meridian...
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What we can (theoretically) do is bend space, which is much more effective.
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Yes but alcubierre's idea of a warp drive is only hypothetically possible. There's a lot of issues with it that we've got to work out.
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Just like there was lots of issues in the way of all other human technological achievements. Though trying to manipulate fundamental physics rather tricky, it's not inherently impossible.
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Ah well we landed man on the moon. Us Americans are ambitious as hell and now with the help of the rest of the national space agencies we'll get it done. Maybe 100-200 years from now.