You could use these in the Pr.Perfect if the info is new for the listener and if no specific time of the action is indicated.
Frankly speaking, sentence 1a) looks odd and incomplete. You know, a lot depends on the context.
A situation for 2a) could be the following: you've just met a former classmate of yours, whom you have not seen for a couple of years and you're telling her all your news.
If you say Last year... then goes 2b).
The PrPerfect is much simpler than the Past Perfect (the more I learn, the less I know but basically all the tenses are easy.