Hi there! I'm also an American PA living with my Canadian spouse/sponsor in Quebec. I had a similar situation to you with my employer, but they decided to lay me off instead of relocate my role even though I had discussed the relocation and work permit with them -- so just be careful with that.
1. Yes. What province you are traveling to doesn't really have any impact on the OWP timeline. The OWP is usually processed through the Edmonton VO. For me, from the time I submitted to the time I received the physical permit took just under 2 months (50 days). My full timeline is in my signature, but I'll put the most relevant pieces for the OWP here for reference:
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Nov 9, 2023: Submitted Inland Spousal PR Application
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Dec 1, 2023: Received AOR
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Dec 10, 2023: Submitted OWP Application
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Dec 20, 2023: PR Biometrics Instruction Letter (applies to the OWP as well)
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Dec 27, 2023: Biometrics Appointment
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Dec 28, 2023: Biometrics marked Completed in trackers
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Jan 22, 2024: OWP Application Status Changed to "Final Decision"
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Jan 23, 2024: OWP Approved
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Jan 29,2024: OWP Received in the mail
2. The CSQ isn't something you fill out, it is a document that essentially says Quebec has authorized you to immigrate to the province, and the Undertaking -- similarly -- is basically a letter that states Quebec acknowledges/approves your sponsor's eligibility and commitment. We received ours in about 2 months (roughly 55-60 days) from the time that the office received our application.
One thing that drove me crazy with Quebec was the lack of transparency in their processing (no trackers or ways to measure updates). For us, the CSQ process was particularly nerve-wracking because my husband is disabled (we had submitted a bit of extra paperwork as proof). My timeline is also a little bit wonky because our credit card failed with the first application we submitted. So for our second one, we did a money order, which had no problems (and tbh was probably easier). We had to resubmit, but we just got the Sponsor Approval and CSQ recently!! I'll condense my CSQ timeline so that you have an idea of how long the processing might take
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Jan 19, 2024: CSQ + Undertaking mailed (included the Postal Money Order with the application -- we also scanned the Canada Post receipt to send it to IRCC via web form as "evidence" of the submission)
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Jan 23, 2024ish: CSQ + Undertaking delivered (not 100% sure on this date since I didn't have tracking details)
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Feb 7, 2024: Payment Accepted (this means they opened the envelope and "cashed" the money order on this date)
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Feb 13, 2024: Confirmation/AOR received in mail (we scanned this letter and sent it to IRCC via web form)
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Feb 19, 2024: email from IRCC acknowledging they received the web form submission
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March 18, 2024: CSQ + Undertaking approved
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March 22, 2024: Received 2 copies of CSQ + 1 copy of CSQ approval letter + 1 copy of Sponsor Approval letter +1 copy of approved application in the mail (all arrived in the same envelope) We also scanned the CSQ and the Sponsor Approval letter (3 pages total) and submitted those to IRCC through web form as well
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March 25, 2024: email from IRCC acknowledging they received the web form submission
If you have any other questions about the CSQ or anything else, let me know! I'm happy to help with any info I can