This answer responds to a part of the question.
1) For both the last two pictures, the satellites, Intelsat 39 and Skymuster, are geostationary communications satellites. We are looking at the Earth pointing face. The images are not especially clear but, approximately the antennas in the centre of the picture are mounted on the Earth face and the outer antennas are more likely set back and deployed off the side of the satellite after separation from the launch vehicle.
2) Each antenna is fed by a horn, or in some cases by a horn with an intermediate subreflector. Its possible that there could be one or several horns for a given reflector, each pointing off it from a different direction to get a different beam on the ground. It is also possible (but not definite) that there could be a phase relationship between the various horns, i.e. a phased array. Its also possible that the horns could be replaced with an array of patch antennas, in which case the phased array relationship is essential. These horns (etc) are facing away from us in the photos, either mounted on a central tower abouve the Earth face or mounted on the East/West walls so as to view the side mounted antennas.
3) The irregular shape of the antennas is indeed to help shape the beam and save power. It is possible this way to put more power over high traffic areas and to guarantee an isolation zone, e.g. so as not to spill over into a neighbouring country.
4) The little white dots. I don't know, I have often wondered. Its seems unlikely that they are sensors as there would have to be a mass of wiring to them and they appear to be little more than bits of tape. They have been visible in photos like this for decades so I don't think bluetooth sensors are in the game. I suspect they are more likely there for measuring the antenna surface properties. I've not seen them on late stage integration photos and suspect they are removed for flight.