You can. But once the SOWP extension is refused, you'll fall out of status in Canada.
Make sure your planned studies in Canada make sense in light of your previous education and work experience and show a progression in studies.
Current processing times apply to everyone. Processing times are not locked in at the time of submission.
If you submit a separate application under Express Entry, this is treated as a completely separate application.
There's going to be no clear / easy pathway at this point. EE is very competitive and nominations have been cut back. Hard to do, but if they can get a job and work permit that should open up doors. Tell them to start learning French now if they are serious about immigrating.
There is no obligation under immigration rules. This only applies under spousal sponsorship. It sounds like you both obtained PR together through an economic immigration stream. Of course she could still pursue you for financial support as you go through the divorce process. However this has...
Ultimately the time to do a comprehensive review and to make updates was before submitting the application. Again, you can submit a new SOP via web form but no guarantee it will be considered.
You can try sending the updated SOP via web form but there is no guarantees they will review or consider it. The SOP you submitted as part of your application should have been the final and not a draft.
You should assume there will be no scholarships available and you will need to pay for your tuition and accommodations costs on your own. Start your research here on how to apply: https://www.canada.ca/en/immigration-refugees-citizenship/services/study-canada/study-permit.html
It's recommend that you have a cultural wedding before applying if at all possible. This doesn't automatically mean you will be refused but then you would want to make sure other part of your application are strong. The fact you have a refused PGWP / are presumably out of status weakens your...