1. 90day/3 month grace period - https://indianembassynetherlands.gov.in/page/surrender/
Look at point number 4 - "There is a grace period of three months after acquisition of foreign nationality (to be counted from the date of registration / Naturalisation Certificate and not from the date of foreign passport) for using Indian passport for travel." You can find this same line on Ministry of External Affairs Website as well -
https://eoi.gov.in/eoisearch/MyPrint.php?0834?001/0005
About Canada exit - I don't think Canada puts an exit stamp, but I could be wrong.
2. Secondly, will Immigration in India allow to board a flight to U.S. on a Canadian Passport? - I have a US tourist visa on my Indian passport. I am hoping I can use that.
3. Lastly, won't it cause any problems when surrendering the Indian Passport as we won't have an exit entry on the Indian Passport ? - I'll exit on my India passport. I don't know if there could be a problem when applying for OCI though. As my travel history will show that I traveled on Indian passport after obtaining Canadian passport.