Yes, you must have nodes. Without nodes you cannot have dummy lines, so that surprises me. In case you do not have nodes, but you somehow (strangely) have the dummy lines, use planarize tool to break your highway line segments at the point that they would intersect with dummy lines. Do the same on the other side to railways lines.
Once you have nodes on highways and railways and for the facilities, you must rebuild your network.
regards,