The "Fill" algorithm seems to treat an Edge.Cut as if it was a trace. This means it will leave a gap equal to the zone's "Clearance" parameter between the edge and the filled zone. Reducing the "Clearance" parameter will reduce this gap. However . . . . the board fabricator will require a minimum "setback" between the board edge and any copper feature (zone, trace, pad, etc). The board-edge setback requirement is typically greater than the copper-to-copper clearance requirement in the layout. Therefore you may want to retain the wide gap at (1).
@Rene_Poschl gave you the solution for this: Change the "Clearance" parameter for the Fill Zone
There is a second (and possibly third) factor to consider here. The Fill algorithm has a "Minimum segment width" requirement. After allowing for the required "Clearance" around the connector pads, the algorithm will NOT fill an area that is narrower than the "Minimum width".
The specific area pointed by your arrow "3" meets the criteria for "clearance plus minimum width", but it is not filled because the fill will be an isolated island, without electrical connectivity to any other copper in the same net.