They are a scam. You don't win "lotteries" you didn't buy tickets in (and you usually don't even win in those you did). You also don't pay "fees" to collect anything. If they were legit they would just take it out of the "winnings". And you want to bet "Jane Smith" isn't her real name?
They will continue to harass you as long as they think they can con you out of your money. YOu cannot believe ANYTHING they say, so do NOT provide them with ANY information. It is best to just hang up.
This is criminal activity. File a complaint with your local police.
If they keep calling, tell them you are recording, and that you have notified the police. Then hang up. Ignore anything they mail you. Since they have continued to harass you, keep it as potential evidence, noting the date you received it. You might also file a fraud complaint with the Indian equivalent of of the postal inspector.