Yes, a US passport holder can travel to Australia.
Yes, a US passport holder needs a visa to travel to Australia.
Practically, it is safe to travel with a legitimate, valid passport of your country. If you are a dual passport holder then you use the particular passport for that country and the other passport for the other country. like if you are travelling to US then use US passport if you are travelling Canada use your Canadian passport.
yes. I need a visa to attend a training in Australia.
Yes.
Yes. As a Lebanese passport holder, you need a visa before travelling to Thailand. http://www.thaiconsulate.ae/en/index.htm
If you are a passport holder of a G7 country you dont need a visa or if you're a passport holder of an ASEAN country member you can visit visa free for 2 weeks.
A passport is generally required in order to identify and show proof of citizenship of the holder when travelling. It is required for security purposes so that the authorities will know who is entering and why he or she is entering their country.
Usually yes, since you hold a British Passport. But of course travelling is safer when you have enough amount of validity in your passport. But if you are returning to your country, it's alright to have just a valid and unexpired passport.
Yes. Threre is no minimum passport validity for EU citizens travelling to other EU countries.
Yes, all west Africans need a visa to visit Australia
If you are a Canadian citizen, then a Canadian Passport would be fine for travelling to these places via cruise ship.