Forget a new work permit, read this:
If CIC received the application for the Open Work Permit BEFORE your current work permit expired, then you are under 'implied status'. This means that: until CIC made a decision about your OWP demand, you can legally continue to work under the conditions of your last work permit, that has now expired. So: the expired work permit is still valid and with that, your SIN is still valid, even though expired. How this works out for the health insurance: I don't know. I suppose it's still valid too, because you still have the legal right to continue to work. If your last work permit was an open work permit, you'll still be able to switch employer during implied status. The only condition is: don't leave and re-enter Canada while on implied status: re-entry will cause implied status to void.
Your lawyer was right, for the OWP you HAVE TO apply by mail. Not to the work permit department, but to the PR department. It can take up to 2 months for the envelope to leave the mailroom and be opened. That's why you should've written "PLEASE ADD TO FILE ASAP", so it could've been sent to the PR department within a week. Now it's probably too late...
The PR card can take up to 10 weeks to make. After landing, the local office needs to send the application to the office that handles PR cards, so it can take a few days in the mail. Than, in the worst case, it takes 10 weeks (almost 2,5 months) and then there'll be a small delay in mailing it to you. Call CIC in another 2 weeks or so if you haven't received it.
@ LY: congrats on the good news for your new job. Happy starting!