We are indian citizen and PR status in Canada.
My son is US Citizen and PR status in Canada.

I come to know from friends and website that USA not allowed dual citizenship for US born citizen.

Like Canada and India allow dual citizenship. So, Indian or canadian born citizen can have Naturalize citizenship of USA and Canadian/Indian born citizenship. But US born citizen can not have naturalize citizenship of other country.

Please let me know is this right or wrong? If right ...

I've decided that when we will be citizen, I 'm not going apply for his citizenship.

My questions are:

1) Is it going to effect his PR status of Canada?
2) He can stay on PR for long time like 12-14 years?
3) If he will go back to India for study, Will he loose his PR?
4) If we are citizen and sponsoring him again to Canada, He will become PR or Citizen?


Thank you in advance...

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Your post does not make much sense.
First of all India DOES NOT have dual citizenship.
Both Canada and the US do allow dual citizenship.
As far as PR status in Canada is concerned, it does not matter which country you are a citizen of, you need to stay the required 2 years out of 5 to maintain it.
So yes, to answer your questions.
1 and 3) He will lose his PR if he does not stay in Canada for 2 years in a 5 year period.
2) Yes you can technically be on/a PR for 12-14 years. Obviously only if you are maintaining your PR status.
4) When you become citizens of Canada, you can investigate whether you can sponsor him for citizenship as a dependant. I am not entirely sure about that.

And please have your posts make some sense in the future.