I have noticed that I tend to fall back when squatting deep(without weights) and if I widen my stance a bit more than my shoulder width I can maintain that squat position with more stability. Now coming back to barbell back squat,will keeping a wide stance be a sort of cheating as glutes are also involved and thus hinder with my leg strength development? I am a 168cm guy,61 kg BW,with max of 90kg and my working set is 80kg x 5,with my current short-term goals as doing 100 kg of 5 reps.Long term goal is to do 2*BW back squat X5 reps.(Also I need to mention that 8 weeks ago I have had an inguinal hernia surgery so I wanna keep my progress slow,steady and safe.
A proper back squat uses a (roughly) shoulder-width stance with toes angled slightly out, which facilitates abduction ("angling out") of the femurs during the movement. Yes, this does use the hips/glutes; this is desirable (not "cheating"!) because it allows us to train more muscle mass. It also prevents impingement of tissues between the femur and the anterior iliac spines, and allows your abdomen to go between your thighs, enabling you to attain proper depth more easily.
Please consider reading more about The Squat.
Sounds like you may have ankle mobility issues. Check this post out which explains how to test and fix mobility issues
The whole website is also a great resource for how to safely improve your squat, as you commented above.
Hope this helps.