Your parents can apply for a tourist visa on their own. There is no law that they must be invited.
I think if you wait till you have a steady job and roots in Canada, and then apply to visit USA, you should have a better chance.
The following statistics released by USDOS note the percentage of B visas that were refused by US consulates world-wide.
Antigua and Barbuda 19.7%
I believe you can take training on B-2 as long as your main purpose of stay in USA is is still medical treatment. Getting paid may be a bad idea.
I dont see much difference in the two (as long as we are truthful with the consulate). Option b may be slightly better because you would already have the L/H visa.
A trip back after just 10 days is likely to be problematic. She can be declined entry because the govt. Can view this is an abuse of B visa in that she is staying in USA more than she is in her own home country.
You should be able to get your green card. Do not travel outside USA until you do. I would suggest getting a lawyer.
B-1/B-2 seems to be the correct visa.
This could be viewed as fraud by the government.
There is nothing in law that stops you from getting an NIV. But grant of visas like B-1/B-2 is completely discretionary.