Your guess B is right, “il” is unpersonnal, you may rephrase it :

J’ai l’impression d’avoir reconnu le sentiment […]
J’ai eu l’impression de reconnaître le sentiment […]

I don’t feel the complexity of the sentence. the “m'” makes it clear the subject is “I”, and “Il me semble” is a very common way to express a doubt, so you recognize it and you know the subject is not “il”.

Using “il” makes the sentence kind of passive, so the narrator is a victim of what happens (all of a sudden, he recognized it). Whereas using “Je” means the narrator does an action to recognize the feeling.

I would have translated it with something like that:

I had the impression that I could distinguish the feeling that was visible on all the faces.

Your Question 1:
The correct meaning is given in your second proposition:

“It seemed to me then that I recognized the sentiment that I read on all the faces.

The “il” of “il m’a semblé…” is exactly your “B” guess: it’s a placeholder meaning precisely “it seemed to me”. So, after “il me semble” you may either place a proposition that must begin with “que” or directly an infinitive verb. It’s that form that surprised you, because it seems to me that effectively this form doesn’t exist in English.

Your Question 2:
In that sentence, reconnaître has no subject, since it’s an infinitive form. But the logical subject is the one who recognises, and here it is “m’” : the narrator.

Your Question 3:
I think that here you are wrong. I can assure you that to a French speaker, that sentence is not messy at all. By the way, the infinitive form of a verb is precisely the one where there is no grammatical subject, don’t you think?