Hey there Swaroop,
Thanks for dropping by! Let me get to your Qs one by one.

1. Will I be eligible for admission into the premier universities with the above credentials? Importantly a 3-year Under Graduation through Distance Education.

Technically speaking you should be eligible. Meaning a 3 year degree is equivalent to a 4 year degree in the US. And yes, distance learning counts as a degree. Will it be as good as someone who went to a Top university in India? No. So you WILL be at a disadvantage. How you can make it up, is something we will have to see.

2. Chartered Accountancy is recognized for pursuing PhD in various Indian universities, does that have a similar impact on foreign universities too?

What counts for a PhD in the US mostly is 1. Your publications and their influence/innovation/importance 2. Your research abilities 3. Your academic records 4. Teaching experience if any. Work experience is of course very important as well, but the major thing they will seek is a good researcher who publishes good stuff all the time.

3. Considering my background, what are the best programs available and what are the various schools that offer the required courses?

Well, before you do a PhD you will have to do a Masters, although often people will do the Masters at the university they plan on doing a PhD (of course in the meanwhile there will be some culling, even within the program). To do a Masters you will need a GRE or GMAT, so that would really be your next step.

4. Does my professional experience (3 articleship at KPMG) affect my admission in any way?
Of course! It's excellent. But for a PhD the academic/research stuff is vital as well!

Hope this helps,
JF