Q. What is the purpose of software testing's - Bug removal, System's functionality working, quality or all?
Ans. The main purpose of Software testing, I think is not to remove the bug but to find the bug. Also ensuring the application works correctly as per the requirements and thereby increasing the quality of the product and increasing the confidence in the product.

Q. Define Quality - bug free, Functionality working or both?
Ans. Quality: The degree to which a product performs as advertised without flaws and without unnecessary complications Also for finding bugs and making sure they (bugs)get fixed and stay fixed.