My wife and I got a Canadian baby while studying M.Sc. in Canada, then we left for PhD in Europe.
Now, the baby is almost 3 years, and we would like to register her for a School in Canada;
1- How can we do that? What are the procedures?
2- What is the Visa type we should apply for?
3- For sure, if we would stay to support the baby, we have to work, ...
Can we benefit from this situation by applying for PR, ...
Having a you child that is Canadian gives you zero benefits. You don't qualify for a visa just because you have a Canadian child and you also don't qualify for a visa just because you have a Canadian child.
If you want to qualify for either a visa or PR - you will have to qualify on your own, just like anyone else. Again, zero benefits from having a Canadian citizen child.
3 years old is too young for school. There is nothing to register her for at this time. You'll have to wait until she turns 4.
You will need to find someone to act as a guardian for your daughter in Canada (this is the person she will live with and who will take care of her since you and your spouse are not entitled to live in Canada).
My wife and I got a Canadian baby while studying M.Sc. in Canada, then we left for PhD in Europe.
Now, the baby is almost 3 years, and we would like to register her for a School in Canada;
1- How can we do that? What are the procedures?
2- What is the Visa type we should apply for?
3- For sure, if we would stay to support the baby, we have to work, ...
Can we benefit from this situation by applying for PR, ...
As scylla has already told you, you do not gain any points from having a Canadian child.
If you want to send your child to pre school, she may be able to start at age 3 depending on when she turns 4. I found this info for Ontario:
Since the cutoff date in Ontario is December 31, this means that children can actually begin school in Junior Kindergarten when they are three years and eight months old. The next level up from Junior Kindergarten is Kindergarten.
If you would like your child to start junior kindergarten before you yourself have a visa to live in Canada, you would need to send her alone and appoint a guardian for her to take care of her while she is in Canada.
Otherwise, keep your child with you, apply for your immigration and move when you are ready. Your child can go to school where you are living whether it is in Canada or somewhere else.