Question2, a): It is not clear what equation we should write, does it refer to the dual lagrangian function ?

The equation that states that the optimal points for the primal and dual problems are equal.

אפשר להרחיב קצת?… במקרה של הדואליות לא ראינו את הפתרון האופטימלי . אפשר לכוון אותנו איפה בדיוק בהרצאה דיברנו על זה?

See 5.1.2 in recitation 5. If the primal problem wishes to minimize $f(x)$ under constraints, we define the dual function $\bar{f}(\alpha) = min_x \mathcal{L}(x,\alpha)$, and the dual problem is find the maximum of $\bar{f}(\alpha)$ under the constraints of positivity of $\alpha$-s. Denote by $x^*, \alpha^*$ the solutions to the primal and dual problems. Then, the equation we're talking about is $f(x^*) = \bar{f}(\alpha^*)$. You need to convert this general case to the specific case we're talking about in SVM.

In this question, do you mean w such that it complies with some constraint? or do you perhaps mean to find the bound on ||w*||?

I dont see any reason that any general w would be bound - this isnt an algorithm like perceptron where w starts at a fixed point and cant "go crazy"

can we still use the fact that w*=sigma(ai*yi*xi)?

I don't know what you mean by "still", the question hasn't changed. You can use whatever properties of w* you need.