Ex 2
The discounted conditional expectation given on the sheet is the final condition used in the Feynman-Kac formula.
For receiving the Black-Scholes Equation, you have to substitute by a function that gives you the required final condition.
Ex 3
Set the options of fzero to
options = optimset('fzero');
options = optimset(options, 'TolX', 1e-6, 'Display', 'off');
and look for values in [0,2].
For debugging:
The first value of the Volatility Surface VS is given by VS(1,1) = 1.4957