Proper compliance in both countries for Canada-based employee of US employer

[JS96]

I am a Canadian being hired under an employee-employer setup with an H-1B visa by a US-based (california) business with no presence in Canada, starting in the fall. It has to be an employee-employer relationship due to the visa. While I’d have the visa to perform work in the US, I'd like to still continue to work out of Canada for the majority of the year (80% canada, 20% US). We were advised that they can't simply pay me as a regular US employee under that setup as the CRA will demand tax for work completed in Canada. We'd like to properly deal with the tax implications in both countries while avoiding double tax withholdings and any penalties. I’m having trouble finding answers on how exactly the setup and withholdings would work. My current, probably incorrect, understanding is:

Canada: The firm would register a business number with the CRA, set up Canadian payroll, and make Canadian withholdings. I obtain a waiver of withholdings to reduce my Canadian withholdings for days worked in the US. I would be issued a T-4 that contains my entire pay. When I file my personal tax, the US income is reported as foreign income and the tax paid to the US is reported as a foreign tax credit.

US: The firm will track and do withholdings for days worked in the US. I may need to give them a w8BEN or another form so they don’t have to do full IRS withholdings. I will be given a W-2 with only my US-source income and withholdings. When I file my 1040NR, I only need to report my US-source income and taxes paid as per my W-2.

Questions:
1) Is this the correct understanding? Is there anything else we need to do or is there a misunderstanding in which forms will be filed or withholdings done?
2) I know that they do CPP/EI withholdings. How does it work for state and FICA? Do they treat it the same way as federal income tax and only withhold for days spent in the US? Do I get a certificate of coverage and the FICA are not withheld at all?
3) How difficult is this for my employer if they’re a small firm with no experience? Are there payroll providers and accounting firms that can make the process much easier?
4) Does it create any Canada income tax return or other Canadian filing headaches for the employer?

5) This is a highly specialized immigration question, but will throw it in the thread anyways in case anyone has thoughts: Does having a W-2 with significantly less income than the agreed upon wage under the LCA create issues for the H1B?

[MarieNugent]

The information you shared is very useful, thanks.