Okay. You’ll definitely need JS (and a set of methods commonly used in it called AJAX) to refresh the page.
For the rest, the Twitter part is a simple matter of using their API. This should be trivial for any developer to do.
For the local news part… local as in “your news” or “news from a provider around somewhere”? If it is your news, do you already have a framework for the distribution of those? If not, you’ll need to think about how to lay this one out, and on this one, a consultant/freelancer may help you. If you’d like to avoid India, drop me an email and we can think this one through together.
If you already have a content distribution platform somewhere, ask them if they have an API that would allow you to read the news from them. If they don’t, you’ll need to build a scraper and pull the news from somewhere already visible. If they do, you’re golden.
This is all relatively trivial. Sadly, I do not know of a ready-made CMS that would allow this out of the box. You may be better off writing your own - or getting someone else to write it.
If you plan on writing it from scratch, here are a couple of useful resources:
