Can we divide phonemes which are specific to a language into some more fundamental entities same across all languages ?
There is the spectrogram (https://en.wikipedia.org/wiki/Spectrogram), maybe that is more fundamental than you wanted. The raw datasets are just .wav or .mp3 files.
None of that is specific to language. The language-specific part is really the transcription and language model on the output side.
Will this help us in achieving language independent acoustic modelling?
Yes, end-to-end approaches (https://en.wikipedia.org/wiki/Speech_recognition#End-to-end_automatic_speech_recognition) make it easier to train and launch models into more languages, and also to train models for macro-languages like Chinese or Arabic.
What are the challenges, if any, in above technique?
Where should we begin? Data, data, data, machines, fundamental challenges of human language like ambiguity and mixed language...
Is there any project using this stuff currently?
Most of them now use deep learning, (https://en.wikipedia.org/wiki/Speech_recognition#Deep_feedforward_and_recurrent_neural_networks), for example https://research.mozilla.org/machine-learning/ (https://github.com/mozilla/DeepSpeech).
There are experiments with universal models and the fundamentals are in favour of it but to my limited knowledge most of the models in production today are still specific to a language. UI or spoken language identification system routes a live input to the hopefully right model.