Okay, I have another japanese desire question?

Question:

This was my original question (scroll down), resloved earlier today, until I saw something weird. Why would someone say, "mizu wo yomushitai"? (I want to drink water) My understanding in the very nice explained anwser I recieved, and my own knowledge, is that it would be "mizu wo yomitai". And if you want to ask someone if they want some water, it would be "mizu wo yomimasen ka?"
Where did this "shitai" come from? Does that mean " do want" or something weird like that?
Again, comments and advice is very helpful. Thank you for your particpation if you choose to answer.


I know how to express desires I want. There is either hoshii, base 2
+ -tai, or if you want someone to do something for you, base te + hoshii.

What really confuses me though, is asking someone what they want to do.
Japanese uses politness and discipline, so to ask someone what they want to do, you put the question in negative form. The problem with that is, I'm not sure how to put it in negative form.

Example: Tabemono wo tabemasen ka?
Do you want food?
Why wouldn't it be: Tabemono wo tabetakunai ka? Since adding tai makes it an i adjective, and kunai is the negative form?
Also, let's say I want to take a walk, or play a game.
Is it: sanpo ni ikimasen ka? Or sanpo ni iktakunai ka, for taking a walk?
For playing a game, is it: Gemu wo yarimasen ka? Or Gemu wo yaritakunai ka?

All advice and comments are appreciated, thank you for taking your time to read. :)

Additional Details
Now since I've recieved two answers, my question is clearer, and more confusing. While you can say, sanpo ni ikanai? Or sanpo ni ikimasen ka? Does that really translate into " Do you want to take a walk?" Because I would of thought it said, " You don't take a walk?" since there is no want in there. Why don't you use the -tai form when asking someone for their desire?
And why is it sanpo no ikanai? Not sanpo ni ikanai ka?

Answer:

First, let's clarify:

Tabamasu ka? = Do/Will you eat?
Tabemasen ka? = You don't eat? (not want)

-masen ka can also be used as an invitation
Tabemasen ka? = Won't you have/eat ? or, Would you like to have/eat ~?

The above are willful action/non-action, not necessarily want or desire (although it might be implied)

The use of the -tai form interjects "want" or "desire"
Tabetai desu ka? = Do you want to eat~?

likewise
Sampo ni ikimasu = go for a walk; Sampo ni ikimasen = don't/won't go for a walk
Sampo ni ikimasen ka? = Won't you go for a walk? Or, Would you like to go for a walk?
even though it's essentially the same in English, we confuse the pattern by saying "like to/want to" because that's how we translate it in English. It may be less confusing if you kept it in its negative form "won't you..."

Sampo ni ikitai desu = I want to take a walk;
Sampo ni ikitakunai desu = I don't want to take a walk
Sampo ni ikitai desu ka = Do you want to want to take a walk?
Sampo ni ikitakunai desu ka = You don't want to take a walk? it cannot be used as an invitation.