So. You were working in Canada for a year on a VR with no work permit and didn't file Canadian taxes. Why didn't you go back and work in India? IRCC will know you were in Canada and working without a work permit for more than 6 months.
You were in Canada on a visitor record. You didn't enter Canada as a visitor and could work remotely without a permit for up to 6 months. You cannot work indefinitely remotely. You would have filed taxes.
So she enters the pool and starts over. She cannot just change streams. She was invited in one stream and it was refused. PNP quota are very low so her CRS score in her EE profile and NOC have to be selected. Tell her to read the application guide as don't know her full profile.
The stream is a job offers stream so the employer must fill out the form with a permanent full time job offer. if employer was never doing that then she applied for a stream she is not even eligible for. She can start over with another stream but what stream is she even eligible for as she is...
They can take as long as they want. There is no clear answer. Depends on if immigration/background check is completed and what countries you have lived in and citizenship. That can take a long time.
You cannot work in Canada as a visitor for a year. Are you counting this work because there will be issues with illegal work in Canada, leaving and not filing taxes.
Or they compare the two letters and look at what you changed not for the better. Or they don't read the new letter at all. You show the opportunities in country of citizenship unless you have PR in another country.
So that is a job offer stream so does she still have a job offer? What does her employer say? You have to ask why she filed for that stream. Maybe not eligible for EE with NOC.
Your highest education is your bachelor degree so that is 7 points. Then it says
"Location of Highest Level of Education Completed in Canada" which is not your diploma.
Hire a lawyer to argue your case.
https://www.alberta.ca/system/files/im-worker-stream-expression-of-interest-points-grid.pdf
What other work permit? There are no others since you came and claimed asylum with no status. Now you cannot apply for H&C for a year and then when you apply processing may take another 2-3 years. You may get a work permit during H&C but that may be 2 years away.
Are you highly skilled? ECA? IELTS?
So what in their own profiles have changed, not you or your husband? Husband cannot sponsor them.
Honestly would consider just one parent applying and see if approved.