Nothing "sends" cookies to your browser. When you visit a web site, it can ask your browser to save one or more cookies, and can request access to information stored in cookies.
The initial purpose of these files was just to store information that could be accessed later to customize the appearance. Think like viewing your webmail online and opening the URL and you see your inbox, with all the subfolders opened up instead of collapsed, or any other site preferences like the checkbox for "save a copy of sent messages in my Sent Items folder".
Since then they've evolved quite a bit, they're used for example to save shopping carts. If you had logged into the site (like eBay) then eBay could store the cart on its end, but if you weren't logged in, you can STILL load up your cart, quit and relaunch the browser, return back to eBay, and your cart will still be there. That's all stored in cookies on your computer.
Adding a bookmark is strictly a web browser function, and I don't know of any web page features that can trigger any browser to create a bookmark. So when you add a bookmark, it should be 100% a browser function and no code or html on the page would have any way of getting activated to work with cookies.
Likewise, any other running web page code (specifically javascript or flash) should be automatically killed by the browser when the page/tab that created it is closed. So once you have all your tabs/pages closed, there shouldn't be anything running anywhere that could be for example, creating a cookie in the background every few minutes.
