The 5th Doctor is allergic to some gases in the Praxis region and the celery changes color to alert him to those gases. When asked what he does then, the Doctor says, "I eat the celery. At the very least, it's good for my teeth." So, you're right on that one.
Sharez Jek is the madman in The Caves of Androzani who becomes obsessed with Peri. It's ironic that the 5th Doctor's best story is his last one. I'll give the gold star, just because you knew it was from Caves of Androzani, and obviously didn't look it up since you didn't mention Jek's name.
Did you know this post has taken me about an hour to write? I shouldn't get started reading Doctor Who stuff, because it takes me an effort to stop. I've read a bunch of stuff about the theories about John Hurt's Doctor, and I think the theory I agree with is the one that's been espoused here, that he's the incarnation between the 8th and 9th and that he's the one who ended the Time War. I can get onboard with a Doctor 8.5.
If you've read The 10 Doctors, Rich Morris' brilliant comic, you know about a Doctor 2.5, between the 2nd and 3rd, based solely on a fan based film (go search on Youtube for Doctor Who Devious). I kindof like and I can get on board with Doctor 2.5, mostly because I buy totally into a season 6B theory, the theory behind how the 2nd Doctor knows certain things that he shouldn't.
Which brings me to some annoyance I have with Jon Pertwee. In the 5 Doctors, there were 2 lines that he spoke that he wanted to have because he thought they would be funny for him to say, but really make no sense at all. For example, when Sarah Jane says something about him not looking like he used to, and he finishes her thought that he doesn't have "teeth and curls". He shouldn't know that! Gah! JNT, who presided over what became a terrible time for Doctor Who, should have stepped in and said no to that.
The 3rd Doctor also has another line in The 5 Doctors that annoys me everytime I hear it, but I can't remember it right now. I know a lot of people like the 3rd Doctor the best, but I do not. He just didn't appeal to me, but, I am going through all the 3rd Doctor stories, so maybe I'll come out on the other side liking him more. Even if I don't, I appreciate that era of Doctor Who, because, without Jon Pertwee, there is no Tom Baker.
Enough rambling. Here's another trivia question.
In The Mind Robber, the Doctor meets a man known as The Master. True or false, this is an incarnation of The Master prior to Terror of the Autons.