If I were in New York and it was Monday night, could I talk to someone in Australia since it would be Tuesday morning or afternoon there?

Yes, of course, but you need a way to communicate with that person such as a phone or computer since talking to someone in Australia from New York just won't work without them.

Of course you can,

Just check local time before calling overseas, so you won't wake someone up in the middle of the night.

They are in a different time zone not in a different time period.

as long as you don't try to talk past the twilight zone

10:00 PM Monday, in Eastern Time is 12:00 PM Tuesday, in Sydney NSW, Australia.
Here's a link you can check:
http://timebie.com/timezone/easternsydney.php
If you have an android phone, maybe you would like to add this widget:
https://play.google.com/store/apps/details?id=tm.app.worldClock&hl=en
If not, there is an app called "timeanddate".

Yes.

Yes, why not? Phone communications have existed around the world for nearly 100 years.

Yes.

Eastern Australia is fourteen hours ahead of New York. So 8.00 pm in New York would be 10.00 am in Sydney or Melbourne.

Yes you can.