(1) What are they going to do now, I wonder?
(2) I wonder what they are going to do now.
I think that "wonder" is intransitive in (1) and transitive in (2).
Am I right?
No: you are not right. "Wonder" cannot take a direct object and hence is always intransitive. Instead, it takes an interrogative clause as complement, as is the case in your second example, where what they are going to do now is a subordinate interrogative clause (embedded question) functioning as complement (not object) of "wonder".
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No: you are not right. "Wonder" cannot take a direct object and hence is always intransitive.
Instead, it takes an interrogative clause as complement, as is the case in your second example, where what they are going to do now is a subordinate interrogative clause (embedded question) functioning as complement (not object) of "wonder".
Why do you think it's transitive?