Part 2; please read part 1 first.

I'd like to learn something about the koala's metabolism and their ability to face deal with the eucalyptus' toxin.

1/ You wouldn't say "about koala's metabolism"; you would only use that form if you were talking about one specific individual. For example "I'd like to learn more about Jim the koala's metabolism". To talk about koalas as a species you would say "the koala's metabolism". The same thing applies to the eucalyptus plant species.

Again, use "the" to refer to a species as a whole.

You may want to bookmark this place:

https://tasmaniandevilunzoo.com.au/

It's in Taranna in south east Tasmania (between Hobart and Port Arthur), and it's involved in a research and conservation program relating to DFTD. I went there back in 2012 and found it most interesting. (As was the Federation Chocolates factory (a small, boutique workshop) just up the road.) You'll also want to see Port Arthur if you're down that way and want to hear some stories; that place is full of them. And if you want a sense of deep history, try Hastings Caves while you're in Tasmania.

I've had to break this into two parts because of Italki's ridiculous character limits. This is part 1.

Australia dreamin'

" Dreamin' " isn't correct English (you never drop the "g" like that), though it's sometimes used in song lyrics and the like to help the word fit better. You can sometimes get away with it if you're using the word more poetically (which is why it may work in in an article like this) but you should be aware that it is non-standard.

After my graduation I'd like to visit Australia.

(Why not also studying in?!).

I'm not quite sure what you're saying there. If you mean that you're asking whether it's possible to study in Australia as well, you wouldn't use "in" as the pronoun. It would be either:

(Why not also study there?) or

(Why not also study in Australia?)

There should really be only one punctuation mark at the end of a sentence. Using both a question mark (?) and an exclamation mark (!) together (or more than one of each) is sometimes done to express excitement but again, it's non-standard.

This country is a kind of biodiversity sanctuary: vegetables plants and animals have had a different evolution way have evolved differently and this make them uniques unique.

1/ The word country is a common noun, and isn't capitalised.

2/ "Vegetables" (verdure) are just a sub-class of plants (piante). The overwhelming number of Australian plants can't be used as vegetables. I suspect that you were coming from the Italian "vegetazione" but the English word that that translates to is "vegetation", which is not the same thing as "vegetables" (but is related to it). You could say "vegetation and animals" but "plants and animals" is more common.

3/ You wouldn't use "evolution" as an adjective (describing the noun "way") like that. It's always used as a noun itself. It's therefore better to use the past form of "to evolve" as I have shown.

4/ I understand why you used "uniques" (because there are many plants and animals, plural) but "unique" is always singular. By definition, it refers to only one thing. In this case it is referring to the entire class or group of Australian plants and animals. not to the individual types.