I'm answering from ndb perspective, I haven't use the search API. All quotes are from your first link.
For 1 and 3 (as ordering is considered part of the original query from cursors perspective):
To retrieve additional results from the point of the cursor, the
application prepares a similar query with the same entity kind,
filters, and sort orders, and passes the cursor to the query's
with_cursor() method before performing the retrieval
So it doesn't really matter how old the cursor is (i.e. how old its query is) since its original query must be restored for the cursor to be obtained.
For 2:
Cursors and data updates
The cursor's position is defined as the location in the result list
after the last result returned. A cursor is not a relative position in
the list (it's not an offset); it's a marker to which Cloud Datastore
can jump when starting an index scan for results. If the results for a
query change between uses of a cursor, the query notices only changes
that occur in results after the cursor. If a new result appears before
the cursor's position for the query, it will not be returned when the
results after the cursor are fetched. Similarly, if an entity is no
longer a result for a query but had appeared before the cursor, the
results that appear after the cursor do not change. If the last result
returned is removed from the result set, the cursor still knows how to
locate the next result.
When retrieving query results, you can use both a start cursor and an
end cursor to return a continuous group of results from Cloud
Datastore. When using a start and end cursor to retrieve the results,
you are not guaranteed that the size of the results will be the same
as when you generated the cursors. Entities may be added or deleted
from Cloud Datastore between the time the cursors are generated and
when they are used in a query.
The Java equivalent page at Limitations of cursors mentions some errors that can be raised for inconsistencies:
New App Engine releases might change internal implementation details,
invalidating cursors that depend on them. If an application attempts
to use a cursor that is no longer valid, Cloud Datastore raises an
IllegalArgumentException (low-level API), JDOFatalUserException
(JDO), or PersistenceException (JPA).
I suspect Python would be raising some similar errors as well.
