I had envisioned something like a sand dollar.
Err, what's one of them, then?
Perhaps the interior is based on a hex grid (more cave-like, less bi-lateral human symmetry).
...sounds familiar, eh, Mr B?

...
I imagined the rooms being larger and perhaps multi-purpose.
No reason why they couldn't be, and there is no canon description of the interior of a Hiver ship to go by (AFAIK).
I imagined more system redundancy perhaps three of everything (bridges, power plants, drives).
There's nothing in any of the books that indicates that's how the Hivers build the components into their ships, but then all that does is give people freedom to design Hiver ships as they think they should be, triple-redundancies and all.
Are Hivers solitary or communal nesters?
Communal. They live in nests of up to 500 Hivers in each, although, once again, there's nothing canon that says "Hivers never, ever live alone".
Does each Hiver “need his space” or do they prefer to “hang out together”?
Hivers work cooperatively with each other, but they also work on their own. I suspect they're very much like Humans.
Those were my first thoughts, so I just wondered what “official” data was out there.
The "hard core" of information about Hivers is actually all in CT AM7; G:T and TNE only adds small amounts of information about the Hivers, and this information complements the information in CT AM7.
Since there are so many versions of Traveller and so much “third party” data, I thought that this was the place to seek enlightenment.
And you were right, atpollard. G:T AR 3 and TNE: AotR are both based on the information in CT AM7. Large parts of both books contain verbatim copies of the text from CT AM7. TBH, G:T AR 3 and TNE AotR compement CT AM7 by adding snippets of additional imformation to that presented (and copied from) CT AM7.
One example of this is the idea of a Terminal Manipulation from TNE AotR:
Terminal Manipulation: The manipulation conducted after the failure of an unsuccessful manipulation to erase all traces of it, or at least all connections to the unsuccessful manipulator. A "coverup".
There's nothing in AotR to say that Hivers didn't do this before the TNE period of the OTU, so we can use the concept in the CT era OTU.