What happens with my data, if I do not enable Privacy Mode in System Settings? What data does elementary OS collect from my device in general? And is the Amazon Web Search which Ubuntu implemented still active?
The Privacy Mode setting under System Settings > Security & Privacy > Privacy is related to local data. There is no data sent online or to elementary. elementary doesn’t collect usage stats through the OS or anything. Privacy mode and the other privacy settings control an OS component called Zeitgeist, which is an open source library that powers local things like the "recent documents" in the Files app or the order of search results in the app launcher.
Turning Privacy Mode on means that the OS will not keep track of usage, making search results less relevant and "recent" type views useless. This protects your privacy from other physical users of your account and is similar to "Private Browsing" or "Incognito Mode" in a web browser.
Leaving Privacy Mode off (which is the default) means the OS will collect usage stats for local use only. The app launcher's search will get more accurate as you use it, the Files app will be able to show a list of recently-accessed files, etc.
Amazon Web Search
elementary OS does not use Ubuntu's Unity or any related code, like the Amazon Web Search. Further, nothing typed into the app launcher's search is sent to elementary or any other third-party. This is true whether Privacy mode is enabled or disabled. It's all kept local.
Ubuntu uses Unity as its desktop environment and this contains the code for Amazon Web Search and collecting data.
elementary OS has its own desktop environment called Pantheon which like most desktop environments remembers recently used files to enable extra functionality in certain applications while using the OS. This data isn't collected and sent to elementary or any third parties. Enabling privacy mode is akin to incognito mode in a web browser. Also the error reporting, which you can decide whether or not to send, is anonymous. Note the following statement on the elementary.io website.
Privacy Mode is not enabled then only non-personal diagnostic data(which you can see if you want to-just click on
More Details when any such dialog box opens) to Ubuntu. Unlike Windows, you can see this sent data completely and this data is totally anonymous-does not even contain your computer's name or Computer Model. And you can even turn it off in relevant settings. Also, the data from the list that is shown on that dialog page(where
Privacy Mode button is there) is stored on your computer only for allowing you to access files, music etc. faster. It is not sent over any network to any servers out of your computer.
The privacy settings are mostly useful when someone is say sharing your account on a corporate network-in which case they can see your past activity if
Privacy Mode is not turned on. But if only use your account, it is safe to keep
Privacy Mode turned off. You can ,obviously, also set up specific apps to prevent data collection from them.