When I applied for citizenship, I never got a call, only letters. First letter told me when and where to come to do my citizenship test. They let me know 2 weeks in advance. A couple of months later, I got another letter telling me when and where to come for oath ceremony. Again they told me 2 weeks in advance.
The Canadian citizenship card has your photo on it, it has no expiry date. It is not a travel document like the PR card. If you come to Canada on your Indian passport with a citizenship card, they might let you in with it but you are really supposed to have a Canadian passport. You also get a citizenship certificate on paper and you need to keep that too because it's the only document that has the date when you became citizen and you might need to know that sometime.
When you applied for citizenship, you applied for the kids too? You sent their photo's? The photos you sent will be used for the card.
You can see what the citizenship card looks like at http://www.cic.gc.ca/english/citizenship/proof.asp
You can apply for passports at http://www.ppt.gc.ca/index.aspx?lang=eng