I am not an immigration expert but will try to answer your questions based on my limited knowledge.
From your earlier thread, it seems that you are on maintained status as you had applied for a study permit extension before the initial one expires. You opted for an extension because you hadn't completed your thesis requirement or received the completion letter.
1. Is it breaking any IRCC guidelines if I wait to get the results of the study permit extension application after the completion of my program AND the expiry of my existing study permit?
Nope, I don't think so as you can continue to be enrolled in your program, including waiting for the result. As long as you are on the maintained status and have sufficient proof of a pending thesis requirement post-expiry of your initial study permit.
2. Do I have to register for the upcoming semester if I submit an extension? Or is it okay not to register for the next term while requesting a "bridging" study permit extension (as they mention many university guidelines for immigration)?
I believe that if you have a pending thesis requirement then you will have to register for the upcoming semester. I am not sure about the registration requirement in case of a "bridging" study permit extension. So please consult your university graduate/undergraduate office or international office about it.
3. If I apply for a PGWP application after getting the outcome of a study extension application (however, after the expiry of my existing study permit AND completion of my studies), will it allow me to continue being eligible to work?
I don't understand what you mean here. If I understand correctly, yes, you can continue to work with your study permit extension till you don't receive your final PGWP. Additionally, after applying for PGWP you will receive a WP-EXT (IMM 0127e) letter that authorizes you to work full-time. But I will point out that you can only apply for a PGWP if you have a valid study permit status.
Best of Luck.