1) Since you are not physically in USA, you don't need work authorization to work for a US employer/customer remotely. This is how all the offshore work is done.
2) Yes, you can earn income from countries outside Canada. Being a Canadian resident, you will be taxed on worldwide income. You have to report this a foreign earned income. US-Canada has a tax treaty to avoid double taxation and in general taxes in Canada are higher so you will end up paying more than what is withheld by US employer.
3) Since you are non-resident of US (after the move), income from job in Canada won't impact your US income or taxes (unless you area US Citizen / Green Card holder who still need to report global income).
This is an over simplified explanation for your case. I am not a a CPA or immigration expert. It would be best if you get in touch with a US-Canada International Tax expert.
Nice way of explaining a complicated issue. I am in the same boat, moved from the US (no longer hold any work visa). My employer who has branches in Canada is asking me to continue working for them remotely. I will continue to get paid in US through the same USD account. Had a few questions hoping you can clarify it for me and anyone else going through a similar situation:
1) Can I continue being paid in my US bank account while working in Canada? (any IRS issues?)
2) Do I need to file US taxes if I am a non-resident/citizen? or do I need to file both?
3) Does my employer have to modify anything in their reporting/payroll/system/immigration given that I am not physically present in the US but working remotely and being paid in USD?
4) Will taxes need to be withheld from my pay given that I am not a resident in US?
5) Are there any regulatory measures I need to be thinking of?
Just to highlight, this is a full-time role that gives 401k, benefits, etc as is with other FTE roles in US.