From the Quran's perspective, jinns are material beings. According to what is popular among Islamic scholars, jinns have a delicate and transparent body and are mainly composed of air and fire and are quick just like the two, thus they are capable to appear in any form they desire. Sometimes they appear as human beings, sometimes as little creatures and sometimes as huge beings with strange bodies, eyes and hair, but is has not been mentioned at all in Islamic references that they have at some time turned into inanimate objects like stones.
For further explanation regarding the characteristics, attributes of jinns and the cause of their creation you may refer to Questions 100 (website: 857), 138 (website: 883), 1296 (website: 1279) and 1097 (website: 1183) of this website.
Regarding how they are able to transform into other forms, jinns have delicate bodies which enables them to take on the form of different things and sometimes, because of certain reasons, Allah (swt) gives them different forms.
Jinns are creatures with delicate and flexible bodies that can contract and expand like air. Sometimes they appear as humans, sometimes as little creatures and other times as huge beings with strange bodies, eyes and hair but however they show themselves, they have only appeared that way, meaning that their essence is the same as before and it isn't that they undergo any change in essence. The only thing that happens is that they are perceived by human senses as the form they have taken on without their essence being altered.[1]
The main element that jinns are made of is fire and due to the light and delicate structures they posses they are capable of transforming into different forms[2] but it has not been mentioned at all in Islamic references that they have at sometime turned into inanimate objects like stones.