Once you call @queue()@, when are the components dequeued into the page hierarchy? When is it safe to call @getParent()@ or use methods such as @isVisibleInHierarchy()@ which rely on component’s position in hierarchy?

The components are dequeued as soon as a path is available from @Page@ to the component they are queued into. The dequeue operation needs access to markup which is only available once the Page is known (because the @Page@ object controls the extension of the markup).

If the @Page@ is known at the time of the @queue()@ call (eg if its called inside @onInitialize()@) the components are dequeued before @queue()@ returns.