> Also, only Tamil has a non-Sanskrit origin and is completely different. Other South Indian languages do have Sanskrit origin/influence.
Recent scholarship around this paints a very different and complicated picture of interactions between Dravidian and Indo-Iranian languages. Specifically, there is evidence that Indo-Iranian speakers and Dravidian speakers exchanged vocabulary even before Sanskrit and Tamil branched off from their parent languages.
From Rice in Dravidian by Franklin Southworth [0]:
> The reconstructed vocabulary of Proto-Dravidian depicts a society whose main source of food is animals and their products. Though the speakers of Proto-Dravidian had some knowledge of agriculture, the absence of reconstructible names for cereals strongly suggests that they were not sedentary farmers at this stage—rather, they were probably herders of sheep and cattle, supplementing their diet with grains and other agricultural products through gathering, trade, and occasional periods of sedentism. The first association of Dravidian speakers with a specific cereal is signaled by the occurrence of the word gōdhūma “wheat” in Vedic Sanskrit, a word derived from a Proto-Zagrosian word meaning “stand of grain”. This word, along with other Dravidian-derived words relevant to agriculture (words for “fruit” and “field, threshing ground”, “joint of plant”) and animals (words for “sheep”, “ass”, “hoof”) suggests a significant role for Dravidian speakers in Indus Valley agriculture. As the distribution of these words in modern Indo-Aryan languages—with cognate forms in Dardic and/or Nuristani languages—is similar to that of inherited words like Old Indo-Aryan “brother” (4 Nuristani, 16 Dardic cognates) or “mother” (four Dardic cognates), it is reasonable to assume that the initial contact between Indo-Aryan and Dravidian speakers took place outside of the Indus Valley, in parts of Iran, Afghanistan, or Turkmenistan, probably at a time when Dravidian speakers were involved in wheat cultivation. Chronologically, this might have been anywhere “from about 3500 BC onwards”, in Bellwood’s words (2005:334, see also Bellwood 2009). The presence of cognates of some of these loans in Iranian languages suggests that both Indo-Aryan and Iranian-speaking groups may have been involved in early interactions with Dravidian speakers.
> By the mid-third millennium BCE, Dravidian had become the dominant language of the Southern Neolithic; the Dravidian languages had split into North Dravidian and Peninsular Dravidian, and the latter was further divided into four subgroups. The Southern Neolithic was “…a system that combined animal husbandry—including the well-known cattle pens (Allchin 1963)—with a new package of crops, of which the staples were legumes and millets, a description applicable to the diet of most South Indians today” (Southworth and McAlpin 2012, unpublished). Its main cereal crops were two millets, bristley foxtail (Setaria verticillata) and browntop (Brachiaria ramosa), whose names were either taken from some unknown language(s) or derived from existing Dravidian words such as ko rr - “food” DEDR 2171. Since South India is not a suitable climate for wheat cultivation, the old word for “wheat” was no longer even a memory, surviving only as Tamil kūlam, a generic term for “grain”, and a few related words in Gondi-Kui (DEDR 1906). When Dravidian speakers today refer to wheat, they use a form borrowed from Sanskrit godhūma, such as Tamil gōdume.
> Contrary to Southworth’s claim (2009) that the language of the Southern Neolithic was a form of “late Proto-Dravidian” (equivalent to what is now being called “Peninsular Dravidian”), it now appears that the Southern Neolithic involved a coming together of various subgroups of Proto-Peninsular Dravidian which had already separated some time previously, had been in intermittent contact over a long period in the interim as each branch developed its own unique crop package, and ultimately pooled their resources to create the collection of crops identified in the Southern Neolithic.
> Regarding rice: the Proto-Peninsular Dravidian word vari-(n)ci, which probably originally had the meaning “seed, grain”, appears first as a word for “barley” in two Nuristani languages. The contact that produced the Nuristani words is perhaps dateable to the same period as that of the word for “wheat”: any time from about 3500 BCE onwards. Lacking evidence to the contrary, it seems reasonable to assume that Dravidian-speaking farmers became part of the population of the Indus Valley from about that time. That they retained that role for a long period of time is shown by the appearance of the OIA words vrīhi “paddy” and “threshed (husked/unhusked) rice” in about 1200 BCE, and by the later replacement of these words by another Dravidian loanword, cāmala/cāvala, a millennium or so later. Additional evidence may come from other names of cereals: for example, Dravidian *co nn al “millet” is the probable source of the late Sanskrit yavanāla (reshaped under the influence of OIA yava “barley”), the source of modern Indo-Aryan words for “sorghum” such as Marathi
[0] https://link.springer.com/article/10.1007/s12284-011-9076-9