Some help for fine details

Hi there,

My website is: http://www.photographyturkiye.com/

Theme: Twenty Eleven, with a child theme

I posted these in my previous post but did not get any replies.
Let me see if I can explain my problems with a snapshot of my website.
Please see this image: (I did this in Photoshop so it is not real. It is how I want my homepage to look)

http://www.photographyturkiye.com/wp-content/uploads/2013/01/website.jpg

What I want to do is:
1. Remove space between posts on homepage (please see snapshot)

2. Add thumbnail to my posts on home page (please see snapshot). I tried a lot of things for this. Searched here or other websites. Added codes suggested. Nothing worked so far.

3.Categories under posts. Pleasee look at the image again and see the category under the post. Can this be done?

Thanks in advance