Can you please tell me I have a pool with plumbing in cooper pipe. I want to know if it is safe to use stabaliser in it(cyanuric acid)?

Yes it is safe to use stabalizer in your pool. You would not be able to maintain sanitizer otherwise as the cyanuric acid (stabalizer) is like sunscreen for chlorine. Copper is not ideal for pool water and no longer used for swimming pool construction. Better start saving your pennies for a plumbing renovation and be SURE that you understand how to balance your pH. If you do not balance the pH well you will almost certainly rot out the copper. It only takes 1 or 2 seasons of bad water. You should read the spa school tutorial at http://www.spachemicalshowto.com

Yes you should maintain your stabilizer at somewhere between 35-45ppm. As far as the copper get rid of it asap. Overtime the copper pipes will dissolve due to unbalanced pool water and it will stain your plaster first starting as blueish or greenish spots and if it gets worse enough it can turn grey on you, meanwhile the plaster is actually being dissolved.