There is also a smaller species, Elephantopus scaber, which is not as invasive but can be mistaken for E. mollis.
In the earlier email, the first of the two weeds illustrated looks like a Crotalaria (Fabaceae) (top, left) but the image isn’t clear enough to be certain. It is likely to be Crotalaria montana which is widespread in PNG and northern Australia and is considered native in both regions.
The second weed in that email looks to be a species of Spermacoce or Borreria (Family Rubiaceae) (image below). Another possibility for this weed is Diodella sarmentosa, tropical buttonweed. This was formerly known as Diodia sarmentosa. Definitely worthwhile trying to get a specimen identified.This group can be very difficult to identify correctly, even with a specimen, so it was suggested to get a specimen to the Lae herbarium.