Yeah, you should be able to do it all in one query. To get the nodes in question along with their relationships you can do:
MATCH (a)
WHERE a.itemId IN ['Q2', 'Q24', 'Q30', 'Q23', 'Q16', 'Q20']
OPTIONAL MATCH (a)-[rel]-()
RETURN a, collect(rel)
That will return you, for each node, an array of the relationships.
Depending on your library that you're using for Neo4j, that may or may not return you something useful to give you the startnode/endnode. You could also do:
MATCH (a)
WHERE a.itemId IN ['Q2', 'Q24', 'Q30', 'Q23', 'Q16', 'Q20']
OPTIONAL MATCH (a)-[rel]-()
RETURN a, collect({rel: rel, start_node: startNode(rel), end_node: endNode(rel)})
That would give you an array for each node containing objects/maps of the data.