Question 1 The circumstance concerns the
part of a whole meaning of fraction. For this meaning, the whole MUST be the SAME for the fractions being compared. Because the pizzas are different in size, it makes no sense to compare the two 1/2's. To say this another way, the two 1/2's cannot be equal.
Question 2 Not conceptually the same thing. 2 parts shaded out of 3 equal parts of a rectangle concerns the part of a whole meaning. That meaning requires cutting something up into equal parts. 2 out of 3 of the videos I own are action movies concerns the part of group/set meaning. This meaning does not require equality of anything; nor is anything being cut up into parts.
Question 3
The indicated division meaning concerns '/' is one way to signal divide.
.8 is the answer to 4 divided by 5.