Ask a Canada Law Question, Get an Answer ASAP!
Have you been living with your girlfriend, and if so for how long?
Are you planning on marrying her? If so, then when?
Once I receive this information I will be able to answer your question fully.
So long as you can prove that you have been common law spouses for at least one year your girlfriend can sponsor you under the spousal sponsorship category.
Here a link to the information you will need about this process:
The way this process works is that your girlfriend will apply to be your sponsor at the same time you are applying for permanent residency status. This is all done through one application. Canada immigration will first asses your girlfriend to be sure she can be a sponsor and once she is approved as a sponsor your application will be processed.
Based on what you describe in your post there is no reason why Canada immigration will not approve the application for you.
It is not going to be a problem because she is sponsoring you as a common law spouse and so long as you are living together it does not matter if she is married to someone else.
You can only get a temporary work permit if the employer, which could be a corporation, applies to the government for a Labour Market Impact Assessment. So it is possible for you to come on a work permit, it is also possible to enter as a visitor so long as your intention is not to remain in Canada. Then if you decide to remain in Canada with your spouse your spouse can sponsor you from within Canada and, in fact, a short time after the application is started you may retain an open work permit which gives you the right to work for any employer in Canada.
But, when you are coming to visit Canada you will have to show that you have strong ties to back home or you will not be permitted to enter as a visitor. These strong ties could include employment in the US, a home in the US, family in the US, etc.