Was the Tor source code trustworthily audited by a third party to check if it does not contain a back-door?
Are such audit results freely available?
Third-party audits are most valuable for closed-source software where there is a restriction on who can look at the source code. In contrast, Tor is open-source so anyone can look at the source code and check for back-doors.
Lots of people have looked at the Tor source code, as can be seen from the number of researchers which have modified Tor and the number of bugs people have found by reading Tor's source. So far nobody has found anything which is close to being a back-door.
Tor also goes through scans by Coverity and Veracode, though these are more for looking for bugs rather than looking for back-doors.
You also have the assurance from the Tor developers:
There is absolutely no backdoor in Tor. Nobody has asked us to put one in, and we know some smart lawyers who say that it's unlikely that anybody will try to make us add one in our jurisdiction (U.S.). If they do ask us, we will fight them, and (the lawyers say) probably win.
I'm not aware of any statements along the lines of "I looked at all of the Tor source code and didn't find a back-door". However, many people have had an opportunity to search for back-doors and the incentive to complain loudly if they find anything suspicious. The fact that nobody has found a back-door is good (but not perfect) evidence that there are none.
What I've said above is about back-doors in the source code, but having source code without back-doors isn't good enough unless you compile Tor yourself. The Tor Project has also been working on deterministic builds, allowing multiple people to verify that the binaries published by the Tor Project match the source code.
TOR was started as a DARPA project and continues to receive US government dollars to this day. To believe that the US government would pay money for an anonymity tool they were unable to bypass or exploit requires an exceptional amount of faith that I lack entirely. I can remember how we sold the well cracked Enigma device to all our allies as the unbreakable encryption device of the 20th century, so that we could decipher their encrypted communications in real time. Tor is the 21st century Enigma machine.
Unless you wrote every line of code yourself and the compiler, along with the OS you are using it on and designed/etched every last one of the chips in your system, you are likely trading information in real-time/clear text for the US government. Excellent security these days just means knowing which governments have access to your connected systems. Consider yourself informed.