The ears of male and female koalas do not differ in any way. The only way koala ears differ is that koalas from southern parts of Australia have ears which have shaggier fur and tend to be browner in colour.
its ears and nose
To protect the inside of the ears from dust and dirt.
Keeping its ears warm.
Yes. Koalas have ears, just as other mammals do, and their sense of hearing is known to be quite keen.
Depending on the predator, yes. Koalas have acute hearing, and can certainly hear ungainly creatures such as domestic dogs, as well as stealthier animals such as dingoes. They would be unlikely to hear a python.
to climb very tall trees
They can but up to 3 feet tall in lenght, and weigh upto 20-30 punds
No. Koalas, which are not b ears, do not live in the river. They live in eucalyptus trees. However, koalas are certainly found in gum trees (eucalyptus) which line many of Australia's eastern rivers.
Listening for danger and possibly keeping cool in that hot climate
Not all types
NO