To answer #2 I don't think you do unless her appearance has changed a lot (like a really different haircut).
Is question 1 about the work permit application?
So whether or not it's considered an indictable offense in Canada is based upon actual Canadian law. But you said this was 13 years ago. When did the sentence end?
I doubt it's the right occupation. What's your NOC? https://www.canada.ca/en/immigration-refugees-citizenship/services/immigrate-canada/express-entry/eligibility/find-national-occupation-code.html
Yes, that's true, you have to re-apply for a PR Card once you're back.
We still have no idea how long it should take but vaccine passports are here now and federal government is enforcing it in November...
It's better to give them permission.
It's reasonable to believe that they are more suspcious of people who want to provide less information. That may not be fair, but I bet that's how they think.
You should be "deemed rehabilitated" based on what you've posted here, which means you can enter Canada.
But it's always safe to find out first. As you can see, you can do so at these places...
I believe you can email the sanned signed copy. But maybe the safes thing would be to submit both your original without the signature and your digital copy with their fresh signature.