How different are the Indo-Aryan languages from the Dravidian ones?
I honestly can't distinguish Hindi and Punjabi from Tamil and Telugu. They're all very similar to each other in my eyes and ears, but that's because I don't have full knowledge about the Dravidian languages. Is there a large difference on their grammar, syntax, vocabulary and phonology? Did they influenced each other on those aspects due to contact and intermixing? How mutual intelligible/unintelligible are they from Indo-Aryan languages?
The Dravidian languages have little to no mutual intelligibility with Hindi and the other Indo-Aryan languages, although both are starting to borrow more and more words from English. I work in Bangalore, where the predominant languages are Kannada and English with large pockets of Malayalam, Tamil and Telugu (and Hindi). Everyone talks about the difficulty of the language barriers here, not just the English speakers. One of our analysts said just this week that as a native Malayalam speaker and long-time English speaker, he can get by in Tamil and Telugu but that Hindi was much more difficult for him to learn a bit.
As for loan words, I threw on a cricket match in Kannada yesterday for grins and giggles and I could understand nothing except I clearly heard the words "confidence", "batting approach" and "spin" along with some other English words mixed in with their commentary. I'm sure some of it comes from simply using the terms of the game in the heat of the moment (e.g., batting approach), but I have a hard time believing some of the other words I heard did not have a translation.
Native English speaker here (American actually learning other languages if you can believe it). Yes, the language barrier is significant, but I'm working on it.
And to your point, many people here in South India speak at least two if not several languages. I would say on average, almost everyone can at least survive in a second language, if not do more. A fairly large proportion of the people can speak two languages and have survival skills in two to four more. Probably half of my office can speak three or more languages -- English, Hindi, and a third language, which is actually their native tongue, such as Malayalam or Tamil.
I've read that most of the South Asians refuse to learn Hindi in order to preserve their languages and culture, as the Indo-Aryans are dominating almost the entire country, same situation with the Catalan and Basque people in Spain. English seems to be the only option to survive there, but not always a reliable one. Are you learning any of the Dravidian languages spoken there?
Dravidian languages are completely genetically unrelated to Indo-European languages, so I doubt there is any mutual intelligibility at all with Indo-Aryan languages beyond recognising shared loan-words (just as an English speaker can recognise English loan-words in spoken Japanese). I don't think the phonology is greatly different, however; a lot of major languages in India seem to share broadly similar phonological distinctions, despite being completely unrelated (probably a result of being in close proximity for a very long time).