No - you are not eligible to work. It is illegal to work in Canada on a visitor visa. You need a work permit in order to be able to work in Canada.
Yes - you can apply to extend your stay as a visitor. There is no guarantee that extension application will be approved.
A visitor visa doesn't qualify you for PR. Whether you qualify to apply for PR or not depends on whether you meet the requirements of one of Canada's immigration programs. Having a visitor visa has no impact on this.