Indexes and inheritance (and access rights)

If I have a collection of tables related by inheritance, is there
any (forced or optional) relationship between indexes on those tables?

For example, if I have a table A with an index Ai, and I create
table B that INHERITS (A), do I automatically get an index Bi on
B with the same properties as Ai? (For that matter, if it's *not*
automatic, can I make it happen somehow? I'd like the index structure
of a table to be part of its class definition, in essence.)

Is there a way to make a single index that indexes records in both
A and B? (For example, to enforce uniqueness of a particular field
globally across A and all its inheritors.)

While I'm on about indexes: it seems I can GRANT or REVOKE access
rights on an index, but what the heck does that mean? Are access
rights on an index actually checked when doing operations on the
underlying table? It would seem rather confusing to do that.

regards, tom lane