creating areas for categories in Home page

I was wondering whether this is possible to implement. Though this is a lot to ask for. But I just wanted to try my luck. I am ready to do all the workaround possible.

Well the requirement goes like this.

Making separate sections for 2 or 3 featured categories.
in the home page after the slider these sections will come. This Section will start with the Category Heading.

Then one of the post will come a bit enlarged way it might be a random selection from the category or it might be the latest post from that category.

and next two or three posts from the category will come in the right of this enlarged one. horizontally.

After all these sections the latest post section will be there.

@alexander I know its a long story. But if you can give me an idea how can I do it. It will be really helpful. Will wait for your answer.

To give a clear picture how the Sections will look like am attaching a screenshot here.

https://www.dropbox.com/s/9k64g7icpbk3773/Post.jpg