If structered as a trust, this might well fall foul of The Rule against Perpetuities, depending on the jurisdiction. See this law review article whre it is said:
Those familiar with the rules of law concerning the duration of trust estates, have learned that private trusts may not be created for unlimited lengths of time. The rule of law controlling the duration of private trusts, is the rule known as "The Rule against Perpetuities." The Law permits the establishment of prvate trusts for only reasonable lengths of time, so as not permanently to withdraw from commerce the realty and personalty bequeathed in trust. The rule
does not apply to charitable or benevolent trusts, as such trusts may continue indefinitely, or, in contemplation of law, perpetually.
See also this Wikipedia article.
It would probably be better to structure such an organization as a corporation, much as The Red Cross is a corporation, or most museums or universities are. That would also simplify handling things for many frozen people.
- What would be an appropriate legal classification?
Corporation.
- How could this entity be structured so it could manage multiple estates?
By simply having a large class of clients, no one of whom runs the corp, any more than any one student runs a university.
- Could this entity choose to keep, say, 30% for internal use e.g. resuscitation research?
Yes, if that was permitted by whatever agreement those preserved had made with the organization, or whatever current law allowed.
- How could this entity be made "recession-bulletproof," such that it could survive collapse of civilization?
I don't see how it could be. Having it hold solid and durable assets would help, against a limited fall, but nothing could insulate agaisnt a totla fall of civilization.
- Could it be given autonomy under the direction of a single person, or even sovereignty along the lines of a Mars colony?
The organizational structure could be whatever the law permits when it is created. A board is usual, but not required. Currently the UN will not recognize as sovereign anything but a nation that holds a geographic territory, but that could possibly change in the future.
- Could it be immune from legal jeopardy if it chose to accept clients who volunteer to be frozen before they die?
That would depend on thee law in such matters, whoch would probably be changed if such freezing became common. Also, if the corporation did not know of this in advance, it probably would not be liable.
- What might happen to the estates if the economy is radically altered, e.g. a scarcity-free system where money is obsolete?
Since its purpose is to preserve property, it is hard to see in what form if any it eould survive such a change.
This sort of thing has been considered in science fiction a few times before, and it is worth reading some of the more notable examples. Why Call Them Back from Heaven by Clifford Simak, Cryoburn by Lois M. Bujold, and The Door into Summer by Robert A. Heinlein all come to mind. The first two deal with the effects on the over all economic and social system to a greater degree.