1. A child born in US, will it get the same benefits in CANADA as their parents?
Yes your child will also become a PR when he/she is sponsored as dependent child
2. Do we have to file PR card application for our child before we enter to canada?
Either one of you ( father or mother) should be in Canada to sponsor the child. But so far you have not landed in Canada after your PR, the principal applicant must enter first or together with other accompanying family members. But your new born baby, after getting his US birth certificate / US passport also can accompany without a visitor visa being US citizen.As a U.S. Citizen your son can stay in Canada without a visa for 6 months. Ask for an extended visitor record at the POE. That could allow the child to be in Canada on visitor status for a longer period. Everything depends to the officer at the POE.
3. Are the health benefits for the child covered as well?
The child will get the health coverage as per the respective provincial rules
4. Will the child be able to avail all the educational benefits?
If you start the sponsorship application as soon as landed, it could take approximately One year for the baby to her PR. So the child should get all the benefits.