Can any darknet activity be traced (by hackers or government) to oneself if one accesses DW from one's own internet that is provided by an ISP that knows one's identity? What about using Qubes with Whonix, VPN over Tor and obfuscated bridges?
When it comes to security or anonymity, we leave the deterministic world for the probabilistic one. The only 100% secure system is a machine with no network, no user inside a bunker with no door. The only 100% anonymous way to visit a site is not to visit it.
If you are a lambda user, unrelated to terrorism, you can do many things without bothering too much for strict anonymity: the chances that somebody watches at you are low. Of course if you plan to buy a kalashnikov in countries where it is illegal to own such a weapon, a VPN or Tor is a minimum, and you must ensure that everything is strongly encrypted. And you also have to hope that you are not connected to a honeypot managed by the police...
If a government is involved, and they specifically watch you, and you are not a highly trained agent, it is too late, you have lost. How can you be sure that the guy sitting 3 chairs from you in an internet cafe is not a policeman?
So it is just a matter of risk. Who do you want to be anonymous from? What is the probability that someone specifically watches after you? What is the risk that the action you are doing will raise red warnings in corresponding security services? (security services here range from your parents or girl friend to the CIA and the NSA).
Anonymity is like security, just a matter of threat you want to be protected from.
One aspect is the internet connection, yes. But you should also consider from what device you access these services. Websites can exploit vulnerabilities in browsers and gain access to your machine in the worst case. I would not use a computer with personal files or other personal information on it as these files, if stolen, could also be used to identified.
The whole point of Tor is of course to make it difficult for adversaries to determine your real IP. That being said, it does not give you 100% anonymity as there are multiple attack scenarios that may still deanonymize you. For example tor nodes might be run by government agencies, and if they manage to spy on your entry and exit node, they may infer your identity.
It all depends on the kind of adversary you're expecting, and the resources you think they will use in order to find out your identity. Although public wifi would make it harder, an adversary that can deanonymize Tor probably will also have the capacity to request any and all video footage near your public wifi (and credit card payments and so on).
Whonix will e.g. protect you against malware that was designed to find out your real IP by breaking out of the Tor browser.
VPN over Tor does not allow you to access the dark web, as in this setup your exit point is the VPN. But maybe you meant Tor over VPN. People tend to question if a VPN brings more security. I personally would not believe them to be perfectly trustworthy, even if they say they don't log.
They could track your IP to your ISP and then the ISP could tell them who used that IP address if they were compelled to.