I wan't to restrict some categories to a group of people that need to comply with some requirements for the category.
They can request subscription, but they'll need to be approved.

This however would be entry level categories where the cost is zero, they are free.

Is it possible to configure a subscription where the cost is zero ?
Or have a payment method associated to a subscription where the payment method is "Free Subscription" ?

Hope i explained my idea properly 

There is no way to pay zero in Osclass Pay plugin.
It always check if fee is defined by checking its price

Is there another option/plugin to restrict access to a category ?
The objective would be to build a set of specialized categories accessible only to approved users, they could request access but need to be approved.

Something like this was suggested here, but I guess the priority is low compared to other things that need to be done.

Having this enhancement would mean that you could create maybe a contact form where users could request access to those special categories, and you would manually add them.
Only then they would be able to see the categories and post listings in them.