Re: what is bias means?
Problem 1.3 proves that PLA converges (to give the correct sign for each training data point) and in steps of size x as you point out (and of size +/1 for the 0 component). As w grows in magnitude the fractional accuracy will improve, and after it has converged, normalizing w[1:] to a unit vector gives the direction vector of the separating plane and w[0] will be its' offset from the origin.
