This will be little more than what's already described in our About and Help Center, but ...
No. If it's not relevant to answering the question itself, then it can be construed as spam, so I would suggest avoiding that. Unlike academia, we're not so much into authored works and privileged groups (comes with too many "human condition" headaches) as we're into building a stack of specific questions on specific topics with open, free to all to access answers. Think of it as volunteering your knowledge for the benefit of all that are interested in the topics defined in our scope, and you might learn something new from it, too. I sure know I have.
Adding links to more restricted access groups of any kind really isn't helpful to our cause. While we do have some limitations ourselves, they're pretty basic and only meant to prevent abuse of our platform for personal gain (e.g. a few reputation points needed to participate in our chats, but anyone can read them, if they're not private), and the rest are earned privileges (i.e. how much the system trusts you that you won't abuse it, earned by helpfulness of your contributions) that you don't require to participate in any form on our website. Any form of sponsorship (academia included) already comes with a stricter set of restrictions, which would clash with the open nature of our platform.
That said, Stack Exchange does allow certain types of advertizing of other groups. You've already mentioned the possibility of advertising one's associations in profile pages (personal choice, I myself don't), and graduated Stack Exchange sites (we're still in beta, so this doesn't yet apply to us) gain the ability to run their own community ads on their site pages, competing for votes and with it rotation space between different community suggested ads, based on how helpful community members themselves find them. All these ads are however disassociated from questions and their answers.
The point being is to keep it simple and manageable; where questions are questions, answers are answers, both complete where they were posted as such, and our main purpose is building a stack of Space Exploration Q&A with the voting system helping communicate to our readers how helpful and relevant have our members found individual contributions.
Anything else should be considered transient (comments are there to identify issues with contributions that should ideally be resolved in the contributions themselves and comments eventually deleted as obsolete, participating in chats is not really necessary and they're meant to strengthen the community and enable other, non-Q&A related activities of our members, our Meta is there to openly discuss site-wide issues, announce new features,... and together with review tasks help the community decide on appropriate actions that the majority agrees with). So everything is community driven. Anyone from other communities is welcome to participate here, and to do so, they shouldn't be required to participate, or be members of any other groups with their own set of rules and restrictions. Feel free to advertise your associations on your profile page, but please refrain from advertising that where it doesn't belong, and is irrelevant to the purpose of your contribution.