Could you explain to me how Tor handles cookies? Thing is that these cookies can carry any and all information about my computer. Things such program details, length and count of every single session on my computer can be transferred directly to the company's web site regardless of how anonymous I am? What I am asking is: Should I still avoid going to the web sites of the companies which software I'm using (without logging in of-course) or not?
In general Tor Browser saves the cookies which come from the originating site and deletes them when you close the browser. You can also click on "New Identity" which will also delete all your cookies.
You can find out about the cookie behaviour when you enter
about:config into the URL bar and search for the term "cookie".
One of the central points is the setting
Network.cookie.cookieBehavior. This controls how the browser allows cookies. Currently it is set to
1 which means "Only cookies from the originating server are allowed".
Network.cookie.lifetimePolicy is set to
2 which means that cookies are deleted at the end of the session.
The developers of Tor Browser have a design document where they describe their policy regarding cookies and other tracking technologies. You'll find further details there.
No, by default Tor Browser allows cookies.
If you disable cookies you will look different from most other Tor Browser users, this means you will be in a smaller anonymity set and therefor less anonymous.
Instead you should use Tor Browser's "New Identity" button located under the Tor Button (Green Onion) menu. This will clear state associated with your current browsing session and unlink your browser from any previous browsing, including any cookies that have been set.
Furthermore, cookies are an integral part of many websites functionality and disabling them will potentially cause unexpected breaks in normal website functionality, for example: the ability to login to a website.
Cookies are only one of the myriad ways in which websites can influence browser state to track you, disabling them will harm your usability, anonymity set and in doing so won't stop websites from being able to track you.
For more information read The Design And Implementation of the Tor Browser.