From your conclusion, 1. is correct. But more specifically, it characterizes the nature of an underlying data generating statistic. A table of results of dice throws is likely iid, but more significantly it is because the dice roll itself is iid.

Not really for 2. since you would be simply calculating for $P(A)P(B) = P(A,B)$ and $P(A) = P(B), \forall A, B$ in the discrete case. Since iid is defined as an iff (if and only iff), this characterization is also sufficient.

Note that the iid assumption allows us to characterize the joint distribution in a certain way, which then allows us to compute it. Otherwise the model might grow to be very complex.

From your conclusion, 1. is correct. But more specifically, it characterizes the nature of an underlying data-generating statistic. A table of results of dice throws is likely iid, but more significantly it is because the dice roll itself is iid.

Not really for 2. since you would be simply calculating for $P(A)P(B) = P(A,B)$ and $P(A) = P(B), \forall A, B$ in the discrete case. Since iid is defined as an iff (if and only if), this characterization is also sufficient.

Note that the iid assumption allows us to characterize the joint distribution in a certain way, which then allows us to compute it. Otherwise, the model might grow to be very complex.