How to create a theme that handle articles in different categories? I am creating a theme that has many categories which have two types of handling articles. 
For example: 


Categories (A,B,C,D,E) will show articles in two column 
Categories (F,G) will show articles in only one column
These articles will show in home page in a different manner 


I had already created page.tpl.php as well as page--front.tpl.php, I also created a node--article.tpl.php. So am I able to do this with drupal theming? or it is not possible?
You will want to create different content types for each type article.

I would then use Views and Panels to create the page. Create a view for each subset of article types then place each view in your panels page.

You could also do it with a theme by creating what panels creates for you but you would still need a view with a block setting and then places the views block in the correct section of your site and set the block to only show on the home page. 

The views+panels is a much cleaner implementation that is theme independent.