Hi Arbolis. I'm a little rusty but let me try to answer some of them. First write it precisely:

where (I think).

To solve this PDE, you generally use separation of variables which is not too bad to learn. Doing that I get:

Now that I have the solution, it's easy to calculate and substitute the point right?

Ok, so you got (1) and (2) and as far as three, then just do a Plot3D[u(x,t),{x,0,10},{t,0,20}] in Mathematica looks to me. and (4) is just . Isn't (5) just at the end points for t=0? (6) is the same dif at x=5 looks to me. (7) and (8) you can do right? As far as (9), just take partials of u with respect to t I think would answer that one.