(i) Is is true that there are areas of mathematics that are closed to people who does not belong to a certain group of professors and students at certain universities?

Theoretically nothing is closed to anybody. Practically, if that group is responsible for some of the most important development, then a beginner in the field, with limited interactions with the leaders has only very small odds of discovering something new.

(ii) If I make the right connections with people working in area B, do you think is feasible to perform my Ph.D research in area B with my supervisor, whose research is just nearby area B, and the advice of a specialist in area B mainly by email?

Theoretically yes, practically difficult. The amount of insight you can get by e-mail is limited. Also, the time that a non-adviser can spend with you is rather limited.

Because I don't know you I am hesitant to advise you. I can only speak of my experience. I have always lived between several worlds. When I started I was about 60% in A and 40% in B. It worked out fine, but I had some challenges. However I always enjoyed the experience.