If Obi-Wan--who was just a student of the art of being a Force ghost--could readily converse with the living immediately after his death, why couldn't Qui-Gon, who learned the trick himself? Did he ever try to talk to Vader over the years after the initial "Anakin, Noooo!" during Tusken massacre? If not, why?
Vader was nearly irreversibly set on the Dark Side path.
Once you go with the Dark Side, forever will it dominate your Destiny - Yoda.
It takes a simpleton moisture farmer son to see any good in him, and it took a threat to his son's life to snap him onto the Light Side of the Duct Tape (remember, fear for family members' life was EXACTLY what made him choose the Dark Side in the first place!).
Therefore, there was absolutely no point in Qui-Gon talking to Vader - he wouldn't have had any hope of talking him out of Sithiness, so why bother?
This is an old question and I'm shocked no one has posted this by now. In regards to the question of Qui-Gon speaking to Anakin since the Tusken massacre, then the answer is...
Yes, he did.
In season 3 of the TV series The Clone Wars, Anakin is visited by Qui-Gon Jinn in the episode "The Ghosts of Mortis". They speak for about a minute about the dilemma Anakin is dealing with in the episode involving the Son. The Clone Wars TV series takes place in between Attack of the Clones where Anakin slaughters the Tusken Raiders and Revenge of the Sith.
The official Star Wars website has a video of their interaction. This is the only interaction I can find between the two characters.
Since this business of "Force-sensitive" seances was established only at the end of Episode III (which was the last "canon" movie to be aired), there was no opportunity for Qui-Gon to haunt the kid from Tatooine that he'd insisted that he'd train on his own if he had to. It has to be left to a "Clone Wars" episode to ever bring this up, and see if Qui-Gon bothers to appear to Anakin. Even then, perhaps later on Vader is either able to shut out any Force visitations or Qui-Gon and/or Obi-Wan don't want to appear to a Sith.
To be honest, it is implied that Qui Gon Jinn does communicate with other Jedis, especially his padawan Obi Wan Kenobi. So based on this info, Jinn could have communicated with Vader, however Darth may have blocked him out.
I think as a force ghost, one can see into the future. It is never said so in the movies or TV shows, but it is kind of implied. If you watch season 6 of clone wars, you understand about force ghosts and how the living force works. Qui-Gon is a believer of the living force. From what I feel, Qui-Gon always knew Anakin is the chosen one.
When Yoda sees a vision of order 66 on Dagobah, Qui-Gon explains that the dark side grows everyday as the clone wars goes on. When asked if there is any hope that the Jedi can prevail, he simply states that there is always hope. This made me feel that he could sense, if not "see", that Anakin will bring balance to the force. It would make sense if he knew about the future, as it would then explain that he knew about Luke and thus knew that even though Anakin would become Vader he would redeem himself. So, he let the events flow in their natural way. Of course he could talk to Vader if he wanted to, as he had managed that in episode 2, but it kind of fits that he knows Anakin is the chosen one and all the events right from episode 1 to 6 and beyond are the will of the living force.
Another way I back up my "he could see the future" argument is by saying that the reason he taught Yoda about manifesting yourself after death, who in turn taught obi wan, is because he knew obi wan's force ghost would lead Luke to Yoda (episode 5). Maybe the reason he taught Yoda was because Yoda required less time to learn, given that he is very strong with the force.