In Sitecore's Rich Text Editor we can add an Image. After adding the image if we right click on it, we get an option "Image Map Editor".
Q1: Where in the Core(Desktop View) can i find this fucntionality/button ?
Q2: How can i bind/link this functionality to a custom button that i built for an image component("Add Image Map" button) ?
The Image Map functionality is part of the Telerik RadEditor control, not Sitecore functionality so it's unlikely you will find any settings for this in the 'Core' database.
If you're looking to extend the default Image field then be aware that Image Map adds lots of additional markup that would not integrate well into the Image field, you would need something much more custom. Add an image to the RTE field and then edit the image map properties to see the markup that is generated. I don't think there are any Telerik controls that just provide Image Map functionality (and you would need a license anyway) but no doubt there are plenty of javascript-based plugins available should you wish to integrate.
The easiest solution may be to just use an RTE field and remove all the other toolbar buttons (usig a custom RTE Profile) except the "Insert Sitecore Media" option.