Problem with connection

It looks a bit like a pencil. Have you looked in the Library here for a pencil? You could download one and see exactly how it was created in the feature tree.

A transition from a hexagon to a circle would most often be done as a loft.

In the example you showed, it is a bit different. My guess is that it was a simple cylinder, then a cut was taken to produce a flat. The cut feature was then patterned about the cylindrical axis to produce the required number of flats.

Probably cut extrude and circular pattern.