Upon the receive of CBSA travel history, can we include it in the application and also pick the check mark in the application to permit CBSA to let them check it themselves if they want or we can use it only to know our history of entries to Canada to make the resident calculation more accurate
You should tick in application form to authorize CIC for CBSA. Your copy is just for your own reference to make sure your residence calculation is correct. Adding a copy with application is one's individual choice. If you add it does not harm. But whether it will help or not depend on officer, if one has lot of travel and provide upfront information with proof officer may find easier to determine residency issue but CIC will collect their own CBSA if they need to whether you provide or not.