Canada is a privacy friendly travel option, with limited data collection for visa exempt countries. Canada does not require biometrics as a condition of entry for many countries. If you hold a US passport, or are eligible for an ETA for your visit, then no biometrics are required to enter Canada. Visa holders and PRs are typically required to provide biometrics.
Data collected during the visa process (if required) will be used on your arrival to verify your identity.
Automated border inspection kiosks, as illustrated above (PIK), are legally mandated only for visa holders and permanent residents. If you are a short-stay visitor without visa requirements, you are not obligated to utilize the PIKs. Please note that these kiosks capture a biometric photograph for 1-1 comparison with your passport, retaining the photograph for 15 years. Staff members may be confused why you don't wish to use the PIK's, however a Privacy Notice on the screens clearly state they are optional.
Canada does retain the data on the RFID chip from your passport, which will contain your photograph at a minimum.
How long will my data be stored?
If you are a short term visitor with no visa requirement, then your photograph is only retained if you choose to use a PIK, in this case the image (without biometric data attached) is retained for 15 years. Your passport photo is likely to also be saved from the passport, however there is no public documentation for this.
If you hold a visa or a PR, data retention guidelines vary and can be found here: https://ircc.canada.ca/english/helpcentre/answer.asp?qnum=714
Who is this information shared with?
Canada routinely shares information with other countries such as: US, UK, Australia and New Zealand - however Canada's Privacy Act does protect your information and requires an immigration related query in order to access your data.
What information is required on exit?
On exit there is no data collection - Canada doesn't run outbound immigration except at Land and Sea crossings, and these outbound crossings are typically a very light version of immigration.