You do not have to wait for the final decision on your Self-Employed PR application before applying for a study permit.
Canada recognizes dual intent: someone can have a permanent residence application in progress and also apply for temporary status as a student. However, you still have to independently qualify for the study permit and satisfy the officer that you will respect the conditions of your temporary stay if the PR application is refused.
For a study permit, you would normally need a letter of acceptance from a designated learning institution, proof of sufficient funds, and in many cases a PAL/TAL, depending on the program and exemptions.
One thing I would be careful about is how the proposed course fits with the profile you submitted under the Self-Employed Persons Program. That program assesses factors such as your relevant self-employed experience, education, age, language and adaptability, and your PR application remains a separate process.
So yes, you can apply for a study permit while waiting. Just make sure the study plan is genuine and well explained rather than presenting it as a way to “make headway” on the PR application.