Interviews are meant to be two-way: The employer is evaluating your fitness for the position. But, employers generally also want to make sure you know enough about them that you can decide if you'll be happy working there or not.
As such, interviewers generally expect questions from candidates. Often, candidates are explicitly allowed time to ask questions, but in general, it's acceptable for questions to come up in the natural flow of conversation, as well.
All that said, it's important to consider that you're being evaluated. Most interviewers will be paying attention to your overall communication style, and that may include making inferences based on how and when you ask questions.
I think you showed some understanding of this when you said,
would it not be good idea to answer the initial question (by the employer, directed at the candidate) in first place, then followed by
You're raising an important point - generally, if you're asked a question, it's OK to get some clarification before you respond - but it's bad form to ignore the question or immediately turn it on the interviewer. So, you should always focus first on making sure you're providing them with a relevant and acceptable answer to their question. However, this can sometimes naturally lead to a candidate "reversing" the question, as well.
So, if you're asked,
Can you give me an example of how you've responded to constructive criticism in the past?
It's totally appropriate to answer, and then ask,
Along those same lines, I was curious - as an employer, do you have any approach to reacting to improvement suggestions from staff? For instance, if I'm working in a team and I have an idea for how to improve a process, how would that be handled?
I'm being careful with wording here - while it may be typical for an employer to provide critique to an employee, it may not be typical in some companies for an employee to critique "upwards" in the personal sense - hence, focusing on impersonal critique (i.e. feedback policy or process) may help put your question in context a little easier.
Ultimately, when choosing what questions to ask, you need to consider their importance to you - and also the potential that a "negative" result may be a good sign. If you ask an employer how they respond to improvement ideas from employees, and they balk and choose not to hire you (because they assume you think you know better, or they assume you'll just complain all the time), that may be a good thing in terms of helping you avoid a situation where you won't be happy. I'm adding this comment because many candidates seem to have a mindset of make choices on how to act in an interview based solely on improving my odds of getting a job instead of the correct mindset which is, make choices based on determining if this is a good fit or not, which means it's OK if they decide not to hire me based on it being a bad fit.