Elfut, if this is you first job as a live-in caregiver, you must apply from outside Canada. For you, in British Columbia, you can take a trip over the border to the Canadian embassy in Seattle.
However, it is challenging to get the first work permit due to the conditions of the live-in caregiver program and the documents required. It will also take time because you will first need a medical check, police clearances, translations etc.
Can I recommend that you take a look at the following web page which is specifically about obtaining your first work permit via the Seattle visa office at
http://www.tlc-edmonton.com/workPermit.html. It provides some useful information that I couldn't find anywhere else.
You can also find answers to your other questions about immigrating via the live in caregiver program at the above site.