Research topics restricted to students at top universities?

Perhaps your advisor had meant merely that the group who work in area B are very strong and have a rich knowledge, and it is difficult for outsiders to enter into or compete with that group because they won't have risen to the high expertise to which that group had brought itself? You seem to present the issue as one of political intrigue and exclusion, but it may not be like this at all. There are surely many mathematical groups, who by working intensely on a focused topic bring themselves to a high level of expertise on that topic. If this is the situation, then it would seem by your other remarks that you can make contacts with that group and begin to study with them and thereby involve yourself in their expertise.

That said, I also believe that it is wise to listen to one's advisor's suggestions about topics of investigation. It may be that your advisor simply feels that he will not be able to help you as much in area B, simply because he doesn't himself have the knowledge necessary to guide you in that area. Thus, your plan to work in area B is essentially amounting to not working with your current advisor, and instead having only an email advisor, who may not ultimately give you the attention that you will want and need later on, and that may not be the best situation. But if there is someone in that group who can server as your mentor, then it may work out.

Regarding questions (i), I think this kind of concern is likely misplaced. In my experience, any mathematician with talent will eventually be recognized for it, regardless of whatever connections they may or may not have.

Another consideration that your adviser might have had in mind is that the experts in area B might be slow to publish or even to write up their work, so that the literature doesn't reflect the state of the art. In that situation, you might find yourself rediscovering what they already know but haven't published. I think this difficulty can be minimized, or even removed altogether, if you can establish really good communication with the people in area B, so that they tell you their latest discoveries, even if they haven't yet written them up. But establishing such a level of communication may take considerable effort on your part.

I hate to break it to you, but academic publishing can be political. The political component is smaller in math than in other areas, but not zero.

Here is a study that shows articles previously published by esteemed psychology researchers were rejected when re-submitted under a different author's name, and not simply because reviewers recognized the articles. The papers were subjected to greater criticism when given a different author.

I don't want to exaggerate the effect of prejudice, just to say it cannot be ruled out.