The background is a bit vague on this one, and has changed over the years, obviously. It used to be that Old One Eye, a special character, was really just a regenerating carnifex from hive fleet Behemoth found entombed on a planet in the ultramar system. To make it 'playable' for other hive fleets too, they invented the reincarnation idea - this got even weirder with the Swarmlord, which somehow had a tactical acumen better than the hive mind itself, but then can be absorbed and rebirthed in a completely different hive fleet half a galaxy away... but still always only one. For the most part, Tyranid players think it's silly to have special characters at all, especially unique ones, and would rather just treat these examples as 'rare mutations'.
As for preserving tyrants and other creatures on 'board' a hiveship... first we should not forget that the hive ship isn't really a ship, but rather a really, really big Tyranid creature itself. Supposedly the brain within the Hive ship are one or more (depending on size) Norn Queens, which do the selective breeding and dna sequencing to adapt to what's needed. Apart from that, a number of other creatures are kept alive and un-absorbed throughout the ship, mostly for defense against boarding actions. Most of these are in suspended animation, sleeping troughout the voyage, but a number of Tervigons are always awake to provide a quick, rapid response force through the birthing of Termagants to slow any assailants until the nastier creatures have been woken from their sleep. It is perfectly viable for a Broodlord to be one of them.
That only specific creatures are taken whole back to the fleet, because of their experiences, seems like an idea that was once thrown in but not really thought through (kinda like the Swarmlord), because as was previously said, all absorbed matter will also be sampled, and all knowledge is already available to every part of the hive fleet within synapse range.