"As a single childless employee, what comparable perks might be available to me when companies offer family / parent perks like PTO for children's school plays for example? Are companies even allowed to designate PTO specifics like what it can be used for? How do I go about asking for comparable perks?"
It sounds like your company offers "family-friendly" policies such as "flex hours" that allow employees to leave work to accommodate responsibilities during normal business hours. If your company offers flex hours, they would be applicable for all employees not just those with children, which means you will be able to use them as well.
Now it's time to ask yourself some tough questions. Do you want comparable perks because there are specific things you want to be able to leave the office to do? Or, do you feel like your time is less valued and protected than those who have spouses and families?
If you have specific things you want or need to do outside of the office, speak to your manager. If they are open enough to allow people to leave for familial responsibilities, it sounds like they would be agreeable to doing the same for you.
Or do you feel that, because you are a single, childless woman, you are expected to work longer and harder than your other colleagues? All of us have a lot to juggle, and the fact that your company lets people leave to take part in these family things is actually really nice. It's not so nice, however, if you feel your time is not as protected as those with children.
You have to be the protector of your time. We all have lives outside of the office, with things that are important to us whether those things are children or a writing class at the local community college. Just like your colleagues are using flex hours to do things for their families, you should feel empowered to use the flex hours to do things that are important to you.
We are happier, healthier employees when we can live full lives outside of the workplace. The fact that your company is giving you flex hours shows that they must believe that as well. If you feel your manager may not take your requests as seriously as those of your familied colleagues, just tell them that leaving for this activity is important to you, and that just like your other colleagues, you will either come in early or leave late the next day to make up the time. It is their policy not yours, and as long as you follow the guidelines of the policy you should feel free to benefit from it.