It is not absolutely necessary in this case to draw a diagram, since the dice have to show different faces we can atually think through this. but let me add a diagram anyway. see below:

notice how i set up the diagram. i put all possible outcomes for one die along the first row, and all possible outcomes for the other die down the first column. the rest of the table shows how they interact, that is, i sum the face of one die and the other. in all, there are 30 possible out comes (since we don't want them to have the same face, we blot out the 6 outcomes where that happens). so now we just count the possibilities we want.

count in the table how many even sums we have, we see we have 12. so this probability is 12/30 = 2/5(i) Probability the sum is even

I think you can do the rest