I am a huge fan of X-Files and I had watched all seasons around 10 years ago. I really want to get into the new show and I enjoy being able to follow the story line very closely. Do I need to watch again the last few episodes of season 9 of 2002 to get back into the show or is the new story rather independent from previous seasons?
This is kind of a loaded question. The new episodes are meant to be a continuation of the old series and they have already made reference to several things from the original series run. That said, I think they have done so with the goal of making the show accessible to those who haven't seen the original series so while knowing the back story will definitely give you a deeper understanding of the new series, I don't believe it is absolutely necessary to have seen them in order for you to understand them.
As an example, the first episode teaser is made up of a voice over of Mulder giving a quick backstory and synopsis of what happened 14 years ago while showing photos of different events. Enough information is given to allow for context that I believe that you should be able to enjoy the new episodes without re-watching the entire original run beforehand although a refresher of a few key episodes might be beneficial if you want to get deeper into the mythology of the series.
EDIT: Having now seen all the new episodes I would say that a general familiarity with the events of seasons 8 and 9 are important to the new episodes, however, as I mentioned originally there is context given to previous events so that new viewers are not completely left in the dark. For a richer experience you should be familiar with the previous episodes but this is not necessary.
New Episodes 2, 3, 4, 5: The "freestanding" monster-of-the-week episodes might make some references to prior events from the old series, they are generally self-contained and as long as you know that Scully and Mulder are FBI agents and work for the Bureau, the rest of the episode is easy to follow along with. Episodes 2, 3, 4 and 5 of the new series fall into this category.
New Episodes 1 and 6: These episodes' storylines are based on the overarching alien conspiracy theme. Familiarity with the characters and history of that 9-year chain of events is helpful but not entirely necessary as the characters give a little background in their dialog for these episodes (having just finished watching episode 6 today).