Number 1, The article is very loosely written with no intellectual thoughts.
Number 2, Niaz this is very very complex thing to analyze and talk about Philosophy of Vedanta or Advaita Vedanta for that matter, What I can tell you Hinduism as a name is new concept, in the sense of its name. The 'ism' has been incorporated to keep it as a religion, It is better known as Sanatan Dharma. There are quite jumber of assertions that can be made from the name how it derived Hinduism, but proper assertion will be still Sanatana-Dharma.
There is mention about the same in some books as well, like The following verse, said to be from the Vishnu Purana, Padma Purana and the Bruhaspati Samhita,
Aaasindo Sindhu Paryantham Yasyabharatha Bhoomikah
MathruBhuh Pithrubhoochaiva sah Vai Hindurithismrithaah
himalayam samarabhya yavat bindusarovaram
hindusthanamiti qyatam hi antaraksharayogatah
Niaz, The Aryan invasion theory as niaz your saying is total wrong but here are my short view on the same, Aryans existed beyond India that is for sure, but they didnt invaded India as it is being said, When river Saraswati dried up a group of peoples moved in the banks of Ganges from Indus, assimilated with new philosophies wrote new books as in upanishads which are more refined than Vedas.
There were several parallel groups of peoples present in India at that time. From Genetics to discoveries of Archeology has proved it however lets not go there it will lenghthen the discussion hugely; On Genetics If you recall Kivisild was second author in the infamous Bamshad study of indian caste populations which had forcefed AIT once but then after the new study he has made a U turn and puted up what actually happened, however if someone says Aryans existed only in India thats a myth, Aryans are a race while what happened in India is a civilization formation which is a part of one race.
I quote Sir.John Marshall, in his book Mohenja-dara and Indus Valley Civilisation, vol-1 Page vi-viii says:
"Taken as a whole, the Indus Valley people's religion is so Charesteristicaly Indian as hardly to be distinguished from still surviving Hinduism....
One thing that stands out both at Mohenjadara and Harappa is that the Civilisation hitherto revealed at these two places is not an incipent civilisation, but one already age-old and sterotyped on Indian soil, wit many millennia of human Endeavour behind it."
Now please note that Hindusthan or Hindu is not from Sindu river, but "the Landmass between Himalyas and Indu Maga Samudram" and this place is Hindustan and people are Hindus and the book of ESTHER of Old Testament calls India as Hodu a minor variation of Hindu.
The vedas say nothing about Aryans or Dravidians and they do not mention anything about foreign invaders as well.
The topic is about Who is a Hindu, then I say the author is mxing up lots of things, in simple terms a Hindu is one who is follower of Sanatana Dharma.
In Sanskrit Arya is used to 'Give Respect'.
It is to be noted that Dravidian gene is present among Aryans in the whole subcontinent, and even Dravidians are not the Tribal peoples who existed in India and still does in many places (I used the term Aryan and Dravidian Gene to simplyfy things but in reality they shoulds not be termed as Dravidian and or Aryan gene as such), My friend Vishnu Som a editor of NDTV travelled in Andaman with Indian Navy after Tsunami, and you know there is a tribe in there called as 'Shompel' Tribe and they are one of worlds oldest living tribes! They are neither Dravidians nor Aryans.
I'll tell you a starking thing, If you know the language of 'Baloch' peoples and see the similarity it has with Tamil, it is quite starking.
You spoke about Durga riding the lion, apparently Being a Bengali it is biggest festival in Calcutta, i.e. Durga Puja, the concept behind it is far from anything Greek, She is among the mythology as goddess but the way she is worshipped is different conept altogather.
Finally Who is a Hindu? the one who worships Ram or Lakhshman? no its wrong, Hinduism is a way of life as you have very correctly put, creation-destruction-preservation and belief in re-incaration, even if I dont believe in these three I cannot be dubbed as a non-hindu.
It is merely a philosophy with elements of Dharma, but one thing is for sure any Hindu should and believes in the Hindu Cosmos.
I'll put up a nice piece of extract here later, and oh Krishna was Black and not Blue and his kingdom was Dwarka whose ruins has been found under the sea by Archeological Society of India.
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Sri I dont agree much with you on the Zoroaster theory, it is known that Persians called us Hapta Hindu from Sapta Sindu.