For e, you need to consider all the different ways of making 4. You are correct in thinking you need combinations of (1,3) and (2,2). Using these "combinations", how many different ways can you add them to get the number 4?
EDIT: Then for 'f', you use a similar thing. Let me explain how they got one.
Let's look at how they got
P(X1+X2=2)=0.01.
The only way you can make 2 = 1 + 1, as you can't get 2 + 0 (as you can't get 0). In other words, you want 1 AND 1, i.e P(X = 1) * P(X = 1) = 0.1 * 0.1 = 0.01.
Now, you use this similar method to get the rest.
EDIT: For 'g', you need to think things through a little. You want the probability of
P(1.5<X1+X2≤3.5.
Now, you know quite clearly that you can't get probability P(X = something . 5). So you only look at integers. Does this make a little more sense in what to do?