We have captured 5 spies. Their names are A, B, C, D, and E

We can summarize this information in a graph, where the vertices are the 5 spies, and two spies are connected if they have worked together. Each spy's assertion is then a claim about the degree of the associated vertex.

Are any of the spies liars?

Have B and C worked together?

I found some approach by drawing a graph of the spies from the lowest number (E = 1) to the highest (A = 4).

So at first we should talk about E. As it comes from the question E have worked with only 1 other spy. So lets see if he's lying or not. If E is lying then he should have never worked with any other spies so then A is also have worked with 3 others which breaks the rules where the question saying At most 1 spy is lying. Therefore E is NOT lying.

Now we move to D. If we consider D as the liar then our graph would be something like the follow, that makes the C or B a liar too. So D is NOT a liar too:

Ok now we get to check if B is a liar or not. As A is the last spy standing so he shouldn't be a liar so the graph would be like this. Considering the following graph one answer is that B is lying:

The question also have another answer but it doesn't mean there is 2 spies lying. As it comes from the question we understand that there might be more than one answer. it says

Are there any spies

As we check A if he is lying or not we can see that A is lying in 2 like below:

And about the second question which asks if B and C have ever worked together or not we can see that C as the never lying spy will have worked with A, E and D and since E will only work with 1 spy so then E and A would have never worked together and that breaks the rule which says only one spy is lying.