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Is it possible that a disconnected graph be an Euler graph ?
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disconnected graph can have an Euler circuit. That's because an Euler circuit is only required to traverse every edge of the graph, it's not required to visit every vertex; so isolated vertices are not a problem. A graph is connected enough for an Euler circuit if all the edges belong to one and the same component

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No, as the basic definition of Euler graph is standardized to only Connected Graphs.

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