Can the financial institution that grants you a loan refuse the loan if you do not subscribe to its insurance?

It is entitled to require that you subscribe to loan insurance. However, you have the right to choose your insurer.
(Act respecting the distribution of financial products and services, s. 22)

When you sign up for a loan and apply for loan insurance, is insurability (conditions for insurance coverage) always checked?

With respect to loan insurance, insurability is often checked at the time of a claim. It is therefore very important to properly respond to questions on the application, particularly with respect to health-related issues. Otherwise, an insurer may dispute and deny a claim.