The verb in A is made by adding たい to the stem form (ます-form).
The verb with the たい suffix is treated exactly like a い-type adjective when used in sentences.
This can only be used to express the desires of the speaker. It cannot be used when talking about what a third person wants or doesn't want to do.
私はカレーを食べたいです。(correct)
弟はカレーを食べたいです。(incorrect)
弟はカレーを食べたがっています。(fixed)
The suffix たがる is added in place of たい, and is conjugated like verbs such as 帰る or 入る(はいる).
When used in the past tense, たがっていた is used, and not たがった.
たい and the third-person
While sentences like 「弟はカレーを食べたい。」 are almost never used in isolation, they can be used to describe the desires of a third person. This can be done when the speaker comes to understand that desire through some other information: the other persons tells them, or they look at the other person and deduce it.
Please look at the following examples:
弟はカレーを食べたいようです。(correct)
弟はカレーを食べたいみたいです。(correct)
弟はカレーを食べたがっている。(correct)
弟はカレーを食べたいと言った。(correct)
Although it varies from person to person, some people might be offended if you use the [PERSON]は[FOOD]を食べたいです when talking about them. The statement is very direct, and they might wonder why you are presuming to state what they want. Again, by using the indirect forms, this can be avoided.
It can sound impolite if the たい form is used to ask about the wants of someone you are talking to (second person), especially if that person if of a higher status than you (and polite forms should be used).
(When offering someone some coffee)
コーヒーを飲みたいですか?(incorrect: inappropriate in some situations)
コーヒーは、いかがですか?(fixed)
(Inviting someone to come with you)
私と一緒に行きたいですか?(incorrect: can be construed as arrogant)
一緒に行きませんか?(fixed)
Note: while it can be somewhat rude to use the たい form when addressing the wishes/wants of those above you socially (bosses, teachers, etc.), this can be safely used with friends in more informal discussion.
Since the ~たい form generally refers to the 1st person, it is not necessary to include the 私は at the beginning of the sentence unless you want to stress that it's you who wants to (do something).
あっ!十二時だから、食べましょう!何がいい?(correct)
ケーキが食べたい。(correct)
お母さんから1000円をもらった。何をしたい?(correct)
ケーキを食べたい。(correct)