Is there any free or purchased library or any API which allows me to update excel sheet while it is opened also.

Is there any free or purchased library or any API which allows me to update excel sheet while it is opened also.

I'm not certain of the nature of your project, but perhaps you could create an Office Add-In? I've had some very good experiences with Add-In-Express: http://www.add-in-express.com/add-in-net/index.php
If just creating an add-in isn't going to work for your application, consider writing a plugin that your application can communicate with to do the work for you behind the scenes.
If you want your Excel spreadsheet to be updated in real time, you have to develop an RTD which can be queried by Excel itself. Please refers to Microsoft documentation for that. Add-In express provides you excellent simplified API to develop that, we are using them and we are very happy with that.
There is no tool that can do that since the file is locked by the operating system.
With COM you should be able to drive a workbook that has been opened by the user.