Just as there is conservation of energy and mass in the universe, so must you also think of "conservation of internal forces". I totally made this term up, it doesn't exist. What I mean by that is that forces and moments never simply appear or disappear.
As you've stated, your beam will present zero bending moment at nodes 4 and 6, where it connects with the left and right columns, respectively. Now, for those columns to present any bending moment at those nodes, the bending moment would have to come from somewhere, in such a way as to explain the discontinuity which would be present at the node (column at node 4 with bending moment, beam at the same node without bending moment). In this case, there is nowhere for such a bending moment to appear.
Therefore, no, the left and right columns will also present zero bending moment at the nodes. The central column depends on how it's linked to the beam. If the column is hinged to the continuous beam, then it'll present zero bending moment. Otherwise, if the column is fixed to the beam, then it will absorb some of the beam's negative bending moment.
Notice that this has nothing to do with the structure's material or with structural design. The solution for internal forces is defined entirely by structural analysis, which is mostly agnostic to such considerations.
As to how to calculate the reinforcement for a column with zero bending moment, one adopts minimal reinforcements defined in codes or, if your country's codes have no such definitions, common practice.
After your edit showing your actual situation, however, let me quote a comment I previously wrote beneath this answer: "A fixed node [...] wouldn't have the narrow throat, but would be a monolithic connection with almost all the column and beam rebar passing through." This connection has no throat and is entirely monolithic (where does the beam end and the column begin? You can't tell because the connection is, well, both) and is therefore clearly, beyond a shadow of a doubt, a fixed joint. Your model shouldn't have any hinges on those connections and, therefore, the beam and the column should both present a (possibly small) bending moment at that point (negative bending moment on the beam, which generates tension on the top fiber. In the column, this bending moment will generate a tension on the external fiber). The bending moment in both will be equal.