I do not recommend mixing retinol with azleiac acid, it's better to use retinol +PHA but also depends on skin.
BHA (salicylic acid) helps with pores, AHA works on surface and such acids are usually called "fruit acids". Azelaic acid is a different ingredient, it's non-photosenstive, it can be used for sensitive skin, it helps with acne and it inhibits tyrosinase aka it helps with pigmentaiton. It can be ever use on rosacea. It's more gentle and it has different built than AHA, BHA or PHA. It is not recommended to use BHA and Azelaic Acid. Also, if you use retinol with any acid - don't use it at the same routine.
It's better to just focus on one active ingredient at the time and once your skin gets used to retinol then try to experiment.