Is it an acceptable practice to perform cardio exercises (about 20-30 minutes) on fasting days when going through an alternate-day fasting program?

Carefully: It is acceptable. It does need to be done with mindfulness. An example of this is in professional football players of muslim faith who practiced during ramadan where they fast from sun up to sun down. Often practices were two times a day. No ill effects were noted. Having said this choosing a time when exercise can be done when heat/ humidity is low is preferable. Hydrate well days off fast.

Do not see a problem: It will probably be better if you have a meal 30 minutes after exercise. Talk to your fitness instructor and nutritionist.