Q5) Proving that something cannot be solved "computationally" is hard work, typically worth a lot more than 5 points. Even Abel and Ruffini in their famous proof about the general solution of quintic polynomials, were satisfied with the very much more modest proof that no solution to those particular kinds of equations was possible with "algebraic numbers".
Providing an answer to this question requires Graduate courses in Computing Theory, Number Theory, Complex Analysis, and Differential Equations.
Q6) Unless the "set of data" mentioned first is infinite in extent, then the discrete set of known data is the same as the set of data.
Q7) Explicit numerical solution of what equation? The one from Q5? But the one from Q5 is not certain to involve multidimensional equations.
Note: multidimensional differential equations are not the same as multivariate differential equations.