The two words have overlapping meanings, so there are contexts where either one could be used. However, there are certain constructs where one would be regarded as much better than the other.
I'm not sure if I can provide an exhaustive list of contexts where you should use might instead of could, or vice versa. Let's start with the example you provided, which is when either word is followed by not.
The phrase might not indicates a possibility that the contrary could happen. The word cannot suggests that the contrary won't happen. And the phrase could not suggests that the contrary wasn't able to happen.
So:
He might not show up.
means that he might show up, but we're starting to think he may not, while:
He could not show up.
suggests that, because of some obstacle, he was not able to make it.
Let's say we're supposed to meet Mike at 8 o'clock, and it's now 8:20. We have no idea where Mike is. I might say:
Let's not wait any longer. He might not turn up.
However, just before I finish my sentence, my cell phone rings. It's Mike! Mike tells me that his flight is delayed; the airplane is having mechanical problems, they haven't even left the runway yet. Mike is 500 miles away. Now, I say:
Let's not wait any longer. He cannot be here; he's stuck in Memphis.
Next, my friend and I leave, and we go to Ted's house. Ted sees that Mike his missing, and asks, "Wasn't Mike coming with you guys?" I might reply:
We waited for him, but he could not be here. His flight got delayed.
This is because, while might infers a possibility, could can infer a possibility, or an ability. Let's say you set a bar a meter off the ground, and ask me if I'm able to jump over it without touching it. I could say:
I might be able to do that. (it's possible)
But now you raise the bar two meters off the ground, and ask me if I can jump over it. I might say:
There is no way I could do that. (it's impossible)
However, there are times when the words could be used interchangeably, as you have sensed. For example, let's say we're leaving the house for a few days, and we're trying to decide whether or not to leave the furnace on. I might say:
Let's make sure the furnace gets turned on before we leave. We might get some cold weather.
or:
Let's make sure the furnace gets turned on before we leave. We could get some cold weather.
In that context, the two phrases mean essentially the same thing.
Now, an interesting example for the advanced reader. Consider these two statements:
The repairman might come today, but he could come tomorrow.
The repairman could come today, but he might come tomorrow.
Is there a difference? I'd say that both of them mean that the repairman is supposed to come either today or tomorrow, although there's a little uncertainty as to which day he will arrive. But does one of them suggest a higher probability one way or the other? I don't think so, at least not reliably.
Best Answer
There is no exact rule distinguishing stall from stand, but looking at the etymology can shed a lot of light. Stall comes from older words meaning a place in a barn where animals stand, especially where a single horse, cow, or pig stands, like this:
This is still the primary meaning, usually listed first in dictionaries. Most of the other meanings are best understood as extensions of this one—even though, in modern life, most city-dwellers never see this kind of stall.
As you can see from this Google search, people make stalls for animals in a variety of sizes and configurations, but most have the following in common: they usually hold one animal who usually stands (sometimes a few animals share one stall), they usually have three walls plus a gate or a wall with an opening where the animal can poke through to access a feeder, they're usually arranged in rows where all the stalls face a path or corridor where a person can walk, and they're usually very spare and modest, serving a utilitarian purpose in a very simple way.
Market stalls, urinal stalls, bathroom stalls, shower stalls, etc. are all similar to animal stalls in obvious ways, but often they don't share all the characteristics. People usually stand in market stalls, urinal stalls, and shower stalls, but they usually sit down in bathroom stalls. As with stalls for animals, sometimes there is no fourth wall at all, as in urinal stalls. All the stalls that I can think of are pretty spare and modest, but if you found a fancy stall, you could still call it a stall, maybe a "fancy stall". Most stalls are placed in rows, but as ColleenV pointed out in a comment, often there is only a single shower stall—but public shower stalls are usually arranged in rows.
The etymology of stand is more obvious: it's just a modest, free-standing structure that serves some limited purpose. There's no analogy with stalls for animals. So, there's not even a loose expectation that stands should occur in rows (though they can), or that they should have little more than three walls (though many do), or even that people stand inside them while using them (though many are like that).
On the left is a typical a hot-dog stand in New York. It has no walls at all! In fact, it has wheels so the owner can move it around easily. On the right is a hot-dog stand that has stood for 73 years. It's large enough for a lot more than one or two people, and it probably has more than one room. Take a look at pictures of newsstands and bandstands for some other typical kinds of structures evoked by stand in this sense. And don't miss the picture of a lemonade stand in Peter's answer: that's another very typical, well-known kind of stand—sometimes consisting of nothing more than a table placed outdoors.
As you can see from the examples, neither stall nor stand implies temporariness or permanence.