In answer to the first part of the question for me it is canon all the way.
That said, I take the view that there are two sides to canon.
The first is hard factual canon, i.e. a character's name, eye colour, height etc. - things that cannot be disputed. Although, given how poor NCIS is at keeping it's own canon, er. canon, writing NCIS fanfic can be a challenge in a way I have not experienced in any other fandom in which I have written.
The second is one's personal interpretation of canon which we back up with factual canon i.e. Gibbs puts his arm around Ducky more than once on the show. I chose to interpret that as them being more than just good friends, a non-Gibbs/Ducky fan would interpret it as just a friendly gesture. In the reverse Gibbs head slaps DiNozzo a lot; I see that as him being irritated by DiNozzo, but I understand many Gibbs/DiNozzo fans see it as a way of him showing his lover affection. Given we have no hard proof either way (we don't see either Gibbs & Ducky or Gibbs & DiNozzo kissing) we interpret the canon to suit us. But it is still canon. And for me it is how I write; I write based on what I see on the screen, albeit with a degree of personal interpretation.
I don't believe I have ever let fanon influence the way I have written, at least not in any major way that completely contradicts canon. However, I do know from what has been said by a number of Fraser/Kowalski fans that a lot of early F/K fiction was based on fanon. People wrote it without having seen the show and when they did see the show, they wondered who Ray Kowalski was and why x, y and z hadn't happened.
As far as the second part of the question, no. I do not believe that it has - or at least I am unable to think of a case of when it has.
13 – Do you prefer canon or fanon when you write? Has writing fanfic for a fandom changed the way you see some or even all of the original source material?
14 – Ratings – how high are you comfortable with going? Have you ever written higher? If you're comfortable with NC-17, have you ever been shocked by finding that the story you're writing is G-rated instead?
15 – Warnings – What do you feel it most important to warn for, and what's the strangest thing you've warned for in a fic?
16 – Summaries – Do you like them or hate them? How do you come up with them, if you use them?
17 – Titles – Are they the bane of your existence, or the easiest part of the fic? Also, if you do chaptered fic, do you give each chapter a title, or not?
18 – Where do you get the most inspiration for your fics (aka 'bunnies') from?
19 – When you have bunnies, do you sit down and start writing right away, or do you write down the idea for further use?
20 – Do you ever get bunnied from other people's stories or art in the same fandom?
21 – Sequels – Have you ever written a sequel to a fic you wrote, and if so, why, and if not, how do you feel about sequels?
22 – Have you ever participated in a fest or a Big Bang? If so, write about your favourite experience in relation to one. If not, are there any you've thought about doing? And if not, why not?
23 – When you post, where do you post to? Just your journal? Just an archive? Your own personal site?
24 – Betaing – How many betas do you like to use to make sure there aren't any major flaws in your fic? Do you have a beta horror story or dream story?
25 – Music – Do you listen to music while you write? Do you make playlists to get into a certain 'mood' to write your fic? Do you need noise in general? Or do you need it completely quiet?
26 – What is the oddest (or funniest) thing you've had to research for a fic?
27 – Where is your favourite place to write, and do you write by hand or on the computer?
28 – Have you ever collaborated with anyone else, whether writing together, or having an artist work on a piece about your fic?
29 – What is your current project or projects?
30 – Do you have a favourite fic you've written? What makes it your favourite? And don't forget to give us a link!