I use the QP solver in the R package kernlab. The solution (number of support vectors) is quite sensitive to the threshold (and why shouldn't it

).

The standard approach in professional applications seems to set it fairly small 1e-12. However, if I go for this choice I probably fail to answer question 10 since the numbers of alphas increase sharply.

I also ran into numerical issues when N = 100. I tried to distort the problem by adding a small diagonal term to the Q data matrix. That solved the numerical issues efficiently but that also changed the solution by returning many more alphas greater than "zero". Now I simply reiterate if the SVM run into numerical problems.

By other properties of SVs - is that related to distances to margin for example? In my "SVM world" almost everything is a result of the alphas.