Your first and primary question is asking if one can completely stop all the data leaks written about there. Like the second part of your question (which has been addressed in other answers here), this first question is practical and answerable. Furthermore, it's answered on that page.
- This is similar to but not quite the same as that question, which is about how to prevent results from appearing. Here, the focus is on options for the user to enhance privacy surrounding Amazon search results, so a wider variety of solutions are presented.
That EFF page is licensed under CC-BY 3.0; its content can be cited and reproduced here as CC-BY-SA 3.0. In case it goes away...
How to Disable Amazon Ads and Data Leaks
You can uninstall Dash's Amazon integration by removing the package
called unity-lens-shopping from your computer. If you are currently
using Ubuntu 12.10. you can click here to open
unity-lens-shopping in Ubuntu Software
Center, and then click the "Remove" button on the right. You can also
uninstall it by opening the Terminal app and typing:
sudo apt-get remove unity-lens-shopping
If you want Dash to only search your local computer and not search the
Internet at all, you can open the Privacy app and switch "Include
online search results" from on to off, as pictured below.
Finally, if you don't like the direction that Unity is going but you
still like the Ubuntu operating system, you can switch to a different
desktop environment altogether such as GNOME
3, KDE, or
You can get GNOME 3 by installing the package called
gnome-shell. You can get KDE by installing the
package called kde-full. And you can get Cinnamon by
adding the Cinnamon PPA to your
and then installing the package called cinnamon. Once
you have installed a new desktop environment, you can choose which one
you want to use from your login screen. Click the Ubuntu logo next to
your username to change your desktop environment.
Source: Privacy in Ubuntu 12.10: Amazon Ads and Data Leaks by Micah Lee (EFF)