Perception of an objects history passing as an observer moves toward it
Yes, it will be 20 Julian years ago.

Yes, it will take 40 years to reach there with speed half the speed of light through vacuum without any obstacles and star must be stationary (though you can't travel with speed of light since physically it's not possible to achieve that speed).

And as you are travelling with speed half to that of the speed of light you will experience a phenomenon of time dilation. Check all the details about time dilation here:

http://en.wikipedia.org/wiki/Time_dilation

You will see time dilated by $\gamma = 1/\sqrt{1-v^2/c^2}$, factor so if you substitute this values it will take you 60 years to reach that star. And it squares all the things.

I hope this explanation helps you. If it is not understandable do let me know; I will explain it in a more mathematical way.