1. Your work permit is probably issued for 2 years at a time. You do not work for a company when you are a live-in caregiver, you work for a family or a person and you live in their home. Caregiver means you take care of children, disabled or elderly. Live-in means that you live where you work. If you want to change employers, you have to apply to change your work permit to a new employer.
2. As far as I know, you can not bring your family when you are a live-in caregiver. You can apply for them when you apply for your PR.
3. You can apply for PR when you have worked as a live-in caregiver for 2 years but you have to do it before 3 years have passed since you first came to Canada to start this job.
4. While your PR application is being processed, you will need to have your work permit extended so you can continue to work and keep your legal status in Canada. You can apply for open work permit at the same time you apply for PR but I don't know how fast you get it. When you get it, you can take any job. When you get your PR, if you applied for your family, they will get theirs too and can come and join you in Canada.
You can find everything you need to know about the live in caregiver program at
http://www.cic.gc.ca/english/work/caregiver/index.asp