How can i make a Slide Show for my Home Page with the following requirements
Views slideshow has solutions to be responsive, see:
http://drupal.org/node/1510526

You can also embed a custom slideshow navigation using views and a global counter in the view, using Tokens you can replace the counter text with whatever you want. An example of this can be found here:
http://blog.urbaninsight.com/2012/01/03/building-slideshows-with-navigation-based-views

All of your criteria are met by Views Slideshow I believe, you just have to get crazy with CSS. I have made the following slideshow with Views Slideshow using the navigation tutorial above, Views, Views Slideshow and Nodequeue.

example view slideshow config


default rendering of ViewsSlideshow in Admin area, an un-themed slideshow


Final themed slideshow with custom navigation


In my case I overlay the navigation into the view, I had to use jQuery to achieve some of the dimensions at runtime and CSS3 stuff for opacity of my overlay div.