1. YES. As long as your employer followed the correct procedures...advertise then apply for LMO + your contract.
2. YES.
3. YES, you can go back to the Philippines and submit there. The thing is, it will take you 14 to 18 months. Saddest part here is, sometimes even if the documents and work experience are genuine, they still reject the application (after waiting for 18 months). Whereas if you are already in Canada, you can lodge your application to NYC visa office. They process WP application of those with valid visitor visa in Canada. I am just not sure how long the processing time is...but I believe it shorter/faster. Meaning, the burden of waiting if you are approved or rejected is shorter/faster!
4. YES. Also, it is better if you have a US tourist visa. Just in case you are called for interview, you can go there without any hassles. Although there are cases when one is not called for interview. I believe WP can be picked-up from the border once approved.