In Canada and yes humanitarian and compassionate grounds. I see that some ppl got through pretty quick after first stage (months after) and others did not even though they had everything in. I guess its based on the officer dealing with your file?
Depending on results of medical, police and CSIS , but if everything ok usually 1-6 months you should became PR and after became PR - the PR card you will receive with in approx three months.
H&C is different from case to case, depends on your application and the factors. If you have the first stage approval then you should be good, the rest will follow soon. I’m wondering did you apply for work permit when you submit you H&C?