Will Humans, the advanced beings on Earth, ever be able to...

...understand the language of Animals?

To answer your question you must understand that humans are not the advanced beings on Earth, but the most intelligent beings. 1) Yes, they can understand
The needs/wants of animals by observing their traits, etc. 2) No, because it is not known wheather animals talk amongst theirselves of not. 3) Actions speak louder that words.

Hope I helped!

There's one thing wrong about your question... language is a quality pertained to humans... not other animals.

Firstly, the correct term is "communication".
Secondly, we already understand some organisms' communication toward one another... for example, dolphins use ultrasound... wolves howl to call for their mates.

Bacteria communicate by excreting signalling proteins.

I've always wondered the same question. I would love to speak to my betta!
I recently watched a documentary where a scientist studied the way dolphins communicated to eachother. They not only used vocalization, but gestures to communicate in different ways. Certain behavior indicated that a dolphin was happy, angry, etc. It was interesting, but the researcher could not find a way to actually speak to them. I believe it is a possibility in the future.