I hope I’m not going to miss any of your (sub-) questions in my answer.
Can you use the construction “wie/was/wo/ob … wohl …?” to express the idea of “I wonder how/what/where/whether”?
Yes, this is basically correct and the wohl is similar to vielleicht. However, they are distinct enough that I wouldn’t use
‘Wie es ihm vielleicht in London geht’ — using vielleicht questions whether he is in London at all or whether he is even going to go there, while wohl implies that he is either already there or practically on his way.
I wonder if it is just a simple matter of leaving “ich frage mich” out from the top of the sentence and only keeping its subordinate clause?
This is indeed the case. German has quite a few possibilities of lone subordinate clauses where the main clause is typically understood to be something along the lines of ‘I wonder (how)’, ‘I can’t imagine (that)’ or similar. For example:
Dass so etwas möglich ist.
This is also a subordinate clause where something like ‘I can’t imagine’ has been left out.
I mean, as opposed to saying: “Wie ergeht es ihm wohl in London?”
This wasn’t really a question in itself but it warrants discussion. Because you can also say ‘Wie ergeht es ihm wohl in London?’ However, using the subordinate clause it is a question you are asking yourself, that you do not expect the person you are talking to to answer (maybe you’re even sure that they cannot know the answer). Placing the verb right behind the question word would make it much more of a question directed towards whoever you’re talking to. It could still be understood as a self-question or rhetorical or whatever but not solely.