Eulerian graph confusing

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Can an Eulerian graph be of edge connectivity 1?

And can an Eulerian graph have vertex connectivity 1?

Please show step how you done it.

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You'd have to go back to your source's definition, but I wouldn't think of a graph with only an Euler trail as being Eulerian. Any graph with an Euler circuit be such that every edge would be part of a cycle and therefore has edge connectivity greater than 1.

But an Eulerian graph can have a cut vertex. For instance, a "bow tie graph" of two triangles that share a vertex would meet that criterion.