Is taking some pieces of fabric from the room designated for academic projects in the institute considered theft, and how can one atone for that?

What you took of the fabric, you are obligated to return it if it is still available, or return its equivalent if it has been damaged, or its value, unless you have been absolved. If you fear harm from informing them, then you are not obligated to do so; it suffices to return the right by any means. If it is impossible to reach them, then give the right as charity, along with sincere repentance.