Takarazuka is famous for opera.

Q1 Not necessarily, it sounds more colloquial to say it without 'its' and it can change the meaning marginally.

Q2 All are fine.

Q3 Yes, all except a are different (a has the same meaning always), but b, c, and d Q2 can be said to mean the same thing or they can be said to mean something else.

Thanks for the help, Wonko.
I'm afraid I don't fully understand what you said. Let me clarify it.
(a) does not have the same meaning as (b), (c) or (d). Is that what you mean?

Which sentence is the closest in meaning to "My brother took the train to go to Kobe"?

Hirashin

(a) Has intent built into the sentence. If you ask the question as to why he got on the train you can answer it with the verb of the sentence and the object, "to go to Kobe". (d) Doesn't imply that Kobe is the final destination of the subject though. For example, "My brother got on a train bound for Kobe. In Kobe he got on a bus to Osaka." Also to me for (b) and (c) they are more about the destination of the train than your brother in my opinion. (b) Can imply that Kobe is the only destination or the last destination but does not specifically state that it is. (c) On the other hand makes me think that there are destinations beyond Kobe but your brother will only go as far as Kobe.

a and your final sentence are interchangeable. (My brother took the train to go to Kobe)

b and c the train is going to Kobe as its final destination but that may not be your brother's destination.

d the train is going towards Kobe but it may not be either the train or your brother's final destination.

Thanks, OoTmaster and Wonko.