It is correct! The second half is rhetorical. "...was he?" only reinforces the question, in a casual way. It can also imply the information you are talking about is not surprising. Here is an example: John: Robert was out drinking again last night. Steven: He was, was he? In this example Steven does not seem surprised. John might go on to tell Steven more about Robert's mischief. If Steven leaves that out, the meaning is the same but the implications are different: John: Robert was out drinking again last night. Steven: He was? This time, Steven seems surprised. John might therefore choose to explain that this is normal behavior for Robert instead of talking about this particular night.

yes. This is a so-called question tag. However, it is more usual to say "wasn't he?", but in some places people use the "positive" question tag, as well. Best, Rüdiger