(1) This really depends if they issue you a visitor visa and how long you stay. If you get a visitor visa there are things listed on it that states your conditions. Things like the things YOU CAN NOT DO (ex: You can't work/study during your visit) I do know on the CIc website and from experience that they will let you study if the course is 6 months and less. However, it really depends on what your conditions the officers gives you.
(2) No, your child will only be a Canadian Citizen and possibly a dual citizen of your country (depending if your country allows that) Ex: Two American couples gives birth to a baby in Spain, the baby is automatically an American, because of it's parents nationality, but also a Spanish citizen, because the child was born in Spain.
(3) As I stated above it depends on the conditions they give you if you are issued a visitor visa, but i do not think it is likely. An LMO is a Labor Market Opinion where the people who are willing to hire you must send in the paperwork to see if they can or not. It is usually approved when there is a job shortage of workers. But like Syclla said it is a long process. If you want to work in Canada go through the skills class. And you can only get a work permit if you have a job offer and this LMo and maybe additional stuff. Also even though you are approved to get the work permit, the officer wherever and however you land in Canada can either give you the permit or not. They need to know if you will LEAVE Canada after your permit is up.