I wish to offer my site visitors some giveaways, however i would like them to be shown only around the website's feed (to advertise it). In other people words, I'm not going it to look like a normal publish on my small website, only around the feeds.

Can there be in whatever way to do that? I understand how to edit my theme files as needed, but when there is a wordpress plugin that does the task, the greater.

Please be aware, the sale is only going to on the feed, not through mail-lists, etc.

This is not a programming answer -- unless of course you particularly wish to request programming-related WordPress questions, you could be best asking on wordpress.stackexchange.com/ -- but I'd only use a wordpress plugin such as the Advanced Category Excluder. You are able to specify any group of publish to become excluded in the archive/home/search pages, or even the feed.

So, install the wordpress plugin, place the posts you need to be feed-only inside a particular category, and configure the course Excluder to exclude that category from everything except the feed.

You will find many plug ins which will append items to the feed, for example:

http://wordpress.org/extend/plugins/copyfeed/

That's most likely what you want if you wish to offer giveaways at the end of every publish. If you would like entire posts, search for some type of category excluder like:

http://wordpress.org/extend/plugins/simply-exclude/

One problem you'll encounter, however, is the fact that sooner or later someone will begin scraping your feed and resale it within an autoblog. That's the case with whatever you do, though.