1.A pregnant woman with a visitors visa in Canada gives birth to a
baby in a public hospital in Canada. After the baby is born what is
the immigration status of the mother in Canada? and as a visitor does
she have access to free medical care in a public hospital?

Hi star73,

1. After the baby is born what is the immigration status of the mother in Canada? 

Her status will be the same as before, no change.   To change her
status, the mother would have to go through the same steps of a Family
Class Immigration application as anyone else. This means that the
child, who is a citizen and resident of Canada, may sponsor the mother
when he/she is 18 years old.

Family Class Immigration
"Canadian citizens and permanent residents living in Canada, 18 years
of age or older, may sponsor close relatives or family members who
want to become permanent residents of Canada. Sponsors must promise to
support the relative or family member and their accompanying family
members for a period of three to 10 years to help them settle in
Canada."
http://www.cic.gc.ca/english/sponsor/index.html

2. as a visitor does she have access to free medical care in a public hospital?

No, I'm sorry, she will not, only citizens and permanent residents of
Canada receive a health card which entitles them to Medicare.

"Canada has one of the finest public health insurance systems in the
world. It is known as Medicare. Under Medicare, you don?t have to
?pay? directly for most health-care services. They are paid through
your taxes.
Medicare is available to all permanent residents and Canadian citizens.
If you do not have a health insurance card, you will have to pay to
receive the medical services you need."
http://www.cic.gc.ca/english/newcomer/fact_health.html

I hope this helps. If you have any questions, please post a
clarification request and wait for me to respond before closing/rating
my answer.

Thank you,
hummer

Search Strategy: I searched the Citizenship and Immigration Canada website.