Simple Question about Particles

Hello all,

I've just started trying to teach myself Japanese, and I have a question. As I understand, the particle 'ka', is used to indicate when someone is asking a question. One of the example conversations from one of the sites I'm learning from get here at some point:

Tanaka: Gakusei desu ka.

Hazuki: Hai, gakusei desu.

Tanaka: Go-senmon wa.

So Tanaka asks Hazuki if he's a student, and the particle 'ka' is present to indicate that he is asking a question. Hazuki replies that he is a student and Tanaka asks what Hazuki's field of study is, but this time he doesn't use 'ka'. Why?

Also, sorry that I'm typing using the English alphabet, I'm still getting to writing properly. I want to learn how to speak first.

Thanks in advance.

"Ka" can be used to make a question, but it is not necessary to use it every time.

The second question could be completed by adding "ka" as in, "Go-semmon wa nan desu ka?" But its longer and formal. Shortening it is a little more casual and convenient, although its not super casual, its just not super formal.

Another method would be "Semmon wa nani?" but its almost childish, esp. in that situation, and definitely too informal considering the apparent familiarity of the two speakers ie, they don't seem to be close friends or relatives.

Thank you! I really appreciate your help.

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Edit:

If I may ask another question in a similar vein, suppose I'm talking about cars and I want to say, "This is the fast(er) one." Would one of the following be correct and are there other was to say it?

Kore wa hayai desu.
Hayai no kore wa.
(or should it be 'Hayai no wa kore'?)

The idea with the last two being, 'This is the one to which the property of being speedy belongs.' Sorry if that's contorted, but I've seen similar sentences and I want to make sure I get the principles.

wa is often used as "compare and contrast," so "Hayai no wa kore" would be correct, as long as you know your leaving off desu.