Short answer: These cases should be true, because the truthness of the conditional proposition in the material implication could be unknown (for comprehension read further; I don't use predicate-logic for explanation).
Introducing summary
The difficulties of understanding the material implication are caused by two things:
a) The intuitive way of alwalys trying to recognise causal relationships.
b) Insufficient expression of the material implication in common natural language.
I will explain the material implication in the follwing using two steps:
1. Give you an analogy to get a conceptual understanding of the way a material implication connects two propositions.
2. Show you why it is reasonable to have the implication always to evaluate as true if the conditional proposition is false.
Step 1: Conceptual understanding of the connection expressed by the material implication
Try to think of the material implication in some perspective as an "one way correlation" ("correlation" like e.g. correlation in statistics). Having two corresponding such "one way correlations" you have a "correlation" (biconditional).
E.g.
$I:$ The banana imports are high.
$B:$ Many babies are born.
Let's assume that both propositions are true. The "one way correlation" "$I\implies B$" says that if the banana imports are high, (at the same time) many babies are born. When we look at the collected data, we see that the banana imports are high and that many babies are born, thus the "one way correlation" is true.
Having two corresponding "one way correlations" ($I\implies B$ and $B \implies I$) we have a "correlation" $I\iff B$. So, when we look at the data and see both has happend (many babies are born and the banana imports are high) we can say, that the "correlation" is true. As you see, obviously the banana imports don't have anything causal to do with the birthrate of babies, still the correlation here is true.
Don't think too deeply about this analogy (as it is difficult to think about the "one way correlation"). Just use the ideas you got on the first impression.
Learning-Question: What is the common feature/ the link/the connection, that couples $I$ and $B$?
Answer:
It is the "same time". The math universe does not have "different times", so everything is always at the "same time". (If you think, there are in some perspective "different times" (read only further if you think that, otherwise the follwing will probably confuse you), then they are just created by you imagining different scenarios. But the logic systems does not have these scenarios, right now in some perspective all truth values are already set [although we maybe didn't found them out yet]. )
Visualisation of the propositional "layer" (I yet don't have enough reputation for embedding). An proposition $P\implies Q$ is only on the propositional "layer"(just a proposition as $\neg P \lor Q$ - it "just" happens to be that $Q$ is true if $P$ is true)[the problem in understanding is that we have to decide the truth values for the implication in general and not on specific cases]. In some sense the causal layer here is the modus ponens.
Step 2: Evaluating an implication as true if the conditional proposition is false
Now after understanding the nature of coupling expressed by the material implication (and therefore by the propositional abstraction) I add some information for the core of your question. And for that I will use a real world example, because that's what we're used to understand. Because our understanding always tries to see causal relations, I will use an example which does have a (real world) causal relationship. But note that this is only in some perspective a "special case" of an material implication as it is additionally of having a propositional relation also has an real world causal relationship [raining and wetness is a "one way correlation" and has a causal relationship]. But that is what we often do: we look at a visual/concrete special case to understand concepts we project on the general case, e.g. if you try to get insights of a field, you might look at the special case of $\mathbb{R}$ on a graph).
$R:$ It rains on the grass of my new friend's garden.
$W:$ The grass of my new friend's garden is wet.
And $L1$ (in the following also named the law 1): $L1:\iff ( R \implies W )$
Assume $R$ and $W$ are true: Now we say "if it rains, the grass gets wet". This proposition $L1$ is clearly true. True enough, but carefully read the sentence again and notice what you are really doing. Probably you are rather evaluating the wetness of the grass ($W$) than you are evaluating the law 1 itself ($L1$).
Now let's say it, it does not rain ($\neg R$ is true) and the grass is wet ($W$ is true). What would you intuitively think, what that says about the truthness of law 1 ($L1$)? In my view, it says pretty nothing about the truthness about law 1 ($L1$), except that law 1 ($L1$) is pretty useless because when it (always) does not rain, what do I care about a law that says something about when it is raining (still it might be true).
You probably know greenhouses/glasshouses. Obviously when there is a big glasshouse above the whole grass (grass of new friend), the grass won't get wet. The problem with that is, we don't know (yet) if there exists a big glasshouse at my new friend's garden (because I yet wasn't in his garden).
$H:$ There is a glasshouse above the grass (we still don't know if it's there or not, I wasn't yet at my new friend's garden).
Additionally we modify $R$ beeing dependent of $H$ (and correspondig $L1$ ):
$R(H):$ If there is a glasshouse, it does not rain on the grass. If there is no glasshouse, it does rain on the garden. ($R(H):\iff \neg H$)
$L1(H):\iff R(H) \implies W$
Now assume it is (always) raining (not necessarly on the grass). Now we have two scenarios. At first we assume there is an glasshouse ($H$ is true), so it is not raining on the gras ($R(H)$ is false). Our law 1 ($L1$) now is pretty useless as it was before, because it tells us something about what happens, when it's raining on the grass (the truthness of law 1 is "irrelevant").
Now we assume there is no glasshouse above the garden, hence it is raining on the gras ($R(H)$ is true). When we now see(while raining on the grass), that the grass is wet, our law is true.
So, assume the law is true. This might be irrelevant to the first scenario with $R(H)$ beeing false ($false\implies true/false$), but the law itself (although pretty useless in that case) is true (as is the material implicaton corresponding to that law).
Assume that the law is false. This is also irrelevant to the first scenario of not raining on the grass ($false\implies true/false$, we cannot say anything about that because our law has nothing to do with that cases). It is just false, because when we see it raining on the grass, the grass is not wet.
As we are handling the law as a junctor, we must decide what truth value the law has, if the conditional proposition is false and the law doesn't say anything to us. Just imagine we would say the law is false in that two cases ($(false \implies true/false)$ is always false). Then $(R(H) \iff W):\iff R(H) \impliedby W \land R(H) \implies W $ would be false if $R(H)$ and $W$ are false. In other words: It rains on the grass if and only if [exactly when] the grass is wet would be false if it is not raining on the grass and if the grass is not wet. We don't want to have that.
I will probably improve this answer in the future as I'm still not completeley pleased and as a good explanation here is important to me.