If you have valid H1b, you can be paid in USD in US. You will pay tax in US first and in Canada later. In canada tax you will claim all the tax you paid already in US.
Yes it is possible. Check with your company/lawyer/university whether they can legally have someone on their payroll who’s not in the country. This is unusual and usually people who are based overseas are paid as consultants on an hourly basis rather than salaried employee, unless the company has a subsidiary there. If you have a corporation set up in Canada check how your company does B2B transfers. Easiest way is for them to just physically mail you a check for your services for that month.
Not sure, it’s probably not as easy as setting up an LLC here in the US, but I could be wrong. There’s something I read online about setting it up as federal entity or provincial entity, and the rules vary accordingly. Canada does not have LLCs but the closest entity would be a ‘corporation’. You’ll probably find online services that would set this up for you.