Genderqueer is sometimes used as an umbrella term, sometimes not. It just means a gender that isn't male or female. Genderfluid is when your gender changes over time. I'm not genderqueer so I'm not really an expert but that's my understanding.
I can only speak to my own meaning of the word genderqueer, but I chose genderqueer over other words to describe myself because it's easier than saying "I am not a man and I am not a woman and my gender does not change so I wouldn't describe it as fluid, but I think I probably have a gender so I wouldn't say I'm agender either?" Again, I don't think that the meanings of the words genderqueer, gender fluid, agender, etc. are exactly the same for everyone you meet.
Genderqueer - Someone who's gender is not male or female. Genderfluid - Someone who's gender can regularly change (eg. male one day, female the next, agender the day after that, pangender next week). Some say that genderfluid is a form of genderqueer, along with agender, bigender, pangender, etc.. These are just guesses, so feel free to correct me if I'm wrong.
Other explanations of them are fine. But do you really have to use the word transsexual rather than transgender? It's falling out of use, and it really annoys me.
Oh, I'm sorry it's just that I ignore most the terms that people use nowadays, they're completely new fore me
I think that genderqueer could refer to gender fluid, but typically means not quite conforming to either gender (non-binary, androgynous) while genderfluid is switching between either gender.