Your questions are indeed related. First let's describe spacetime as like a stack of photos, the photos being different times. Real things are in some region of one of the photos and in a possibly different region of a different photo but don't jump discontinuously from one region to another in between two individual photos. Note this is an analogy and lots of things are wrong with it but it might help for this situation. And imagine that it is a magic camera, more like a picture still from a video game, one that isn't about light that got to some camera or eyeball location at some time but is really just a picture representing the ways things are at a kind of moment.
So in this kind of a photo you might see a wormhole. But the wormhole is entirely capable of being inside a region of curved spacetime that is intensely curved, like near a black hole, and so if you watched a series of photos you might notice that the clocks people far away carry tick rather fast compared to the clocks near the wormhole, you need to look through a few to watch a clock far away tick but you have to look through lots and lots of photos to watch a clock near the wormhole tick. And that is precisely because a wormhole has very curved spacetime, just like a black hole (really it is about the relationship via the curvature of the far away region and the close by region).
This means that a wormhole that forms and has just a few ticks of clocks for the things in the middle could exist for people on the outside for a very long time. That's nice for people that want to say they own a wormhole that is far away, the wormhole can last a while.
But when you get near you lose that advantage, you and the wormhole age more in sync. So you could imagine in the photo a whole bunch of people, some just entering, some already inside, some in the middle, some close to existing the other side some existing the other side. But if you look at later photos you see the wormhole crushes itself before the people entering manage to get out. And you see the people that exited came from the same side they entered, they were inside and heading out but they didn't come through from a side different than the one they come out.
And this seems to be pretty generic, regular matter tends to warp spacetime to make it do this pinching off when it gets strongly curved. It is what General Relativity describes inside a black hole.
There isn't an accepted and well known way around it. If you had some exotic matter that curves spacetime differently, you might be able to keep it from pinching off. And people research how to get away with using the least amount of it, but that might turn out to be harder if you then have to smear it into really thin sections.
So the throat that connects the two regions seems to pinch off rather quickly from the perspective of things inside it. By the time you wait for it and then enter one side and then get to the middle it is too late, only things that were already in the middle before you were had time to get out.
So the magic photos shows a connection if you look at a single photo. But to any of the regions in the photo corresponding to stuff, these things that have to move through time to get somewhere else the wormhole closes because it has enough local time to get to the other side. So by the time you flip through enough photos to see a photos with it deep inside, it has already closed off too much. To things that have to move through time, you can't get across.
It is like if the US decided to legalize the transportation of X anywhere across the country but they did it at 8am pacific 9am mountain 10am central and 11am eastern and they only allowed it for 5000 nanoseconds starting at that time. That's enough time that each part of the country might be able to move something a mile, but there is just no way to have something enter the west coast near sea level and get to the east coast while it was still legal. At some theoretical snapshot it looks like there is a path from one coast to the other, but it just doesn't last long enough to actually get from one end to the other during the window of time.
That's what happens in a wormhole that pinches so fast as to not be traversable. Specifically they compare the length from one end to the other and the time (as measured by clocks inside it) it stays open before it gets pinched. For the US, it is much larger than hundreds of miles wide so thousands of nanoseconds just isn't enough time to get across (light goes about 30cm in one nanosecond). The ratio of the length to the time is too big if it is much bigger than the speed of light. For most wormholes studied that are made out of regular matter they are too long compared to how long they stay open.
Think of it this way, making them longer seems to pinch them off quicker. And the length is through the wormhole, not how far apart the ends are in the pretty flat region, that is a totally separate issue.