There are a couple of things going on here but the major update you need to the traversal is to use a project() step instead of a select().
select() and project() steps are similar in that they both allow you to format the results of a traversal however they differ in (at least) one significant way. select() steps function by allowing you to access previously traversed and labeled elements (via as). project() steps allow you take the current traverser and branch it to manipulate the output moving forward.
In your original traversal, when there are no outgoing edges from original v so all the traversers are filtered out during the outE() step. Since there are no further traversers after the outE() step then remainder of the traversal has no input stream so there is no data to return. If you use a project() step after the original v you're able to return the original traverser as well as return the edges and incident vertex. This does lead to a slight complication when handling cases where no out edges exist. Gremlin does not handle null values, such as no out edges existing, you need to return some constant value for these statements using a coalesce statement.
Here is functioning version of this traversal:
g.V().hasId(3).
project('v', 'e', 'child_v').
by(valueMap()).
by(coalesce(outE().id(), constant(''))).
by(coalesce(out().id(), constant('')))