Open Work Permit Applying for CSQ/PEQ

[taisoares]

Hi,
I have few questions and I hope someone can share suggestions or ideas to help me with this situation.
I am filling the form to request CSQ, under PEQ - temporary foreign worker

- I have a open work permit valid until August 2019
- this work permit is connected to my ex husband, he has a Post-Doctorate Work Permit same expiration date
- we divorced in May 2018 and my name is back to maiden name, no need for this last family name
- the divorce certificate shows that my name back as before getting married, and I have not updated my passport or any other ID yet

Questions:
- Do I need to I update my Passport and other IDs before applying for CSQ with my maiden name? Or just attaching the divorce certification is enough?
- Can I just update all documents with my maiden name after receiving my Permanent residency?
- I am divorced since May 2018, does it affect the Open work Permit I have if I am working full time right now?

Thank you in advance!