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My initial idea was that maybe there was a info node for that, but I don't think there is...

So, then I thought that maybe it could be done using raycasts? That go off on each vertex and the two first (smallest edge) / last (biggest edge) to find another vertex are the ones? Raycasts are something I never explored and I also have very little knowledge on indexes (for selecting the vertices).

Basically the use case was to get the length of that edge, but to make it more versatile for other situations it would be useful that it could also select the exact points on a index that correspond to those ones.

Could anybody help me with this, please?

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Here's one (lowest index) shortest edge and one longest edge (also lowest index):

If you want to get all edges that have length equal to the shortest edge (ex æquo shortest) just get rid of the Delete Geometry node. Otherwise you can repeat the setup to use a 2nd criterion, 3rd criterion and so on.

Since similar questions appear often, here's a generalized version to get the (ex æquo) smallest elements of geometry:

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