助け
助け means help in 助けが必要です, so the speaker says that help is needed. It is the thing marked by が and described as 必要です. Use it when asking for or referring to help in a polite situation.
が
が marks the thing that is needed or wanted in this dialogue: 助けが必要です, 水が必要です, and これが欲しいです. It commonly follows the item before 必要です or 欲しいです. Use this pattern when stating a need or desire politely.
必要
必要 means necessary or needed in 助けが必要です and 水が必要です. Together with です, it says that the following or preceding item is needed, rather than simply naming the item. A useful pattern is Xが必要です, when you need something in a practical situation.
です
です makes the statements polite in 必要です, 欲しいです, and 好きです. Here it follows the description of a need, desire, or preference and gives the sentence a polite ending. Use the complete forms from the dialogue when speaking politely about what you need, want, or like.
水
水 means water in 水が必要です, where the speaker says that water is needed. It is the thing marked by が before 必要です. Use it when asking for or explaining a need for water.
これ
これ means this or this one in これが欲しいです and これは好きです. It points to an item understood as being near the speaker or currently selected. Use it when identifying one item before saying that you want or like it.
欲しい
欲しい expresses that the speaker wants the item in これが欲しいです and あれが欲しいです. The desired item is marked by が in both sentences. Use it when choosing or requesting something, with the desired item in the position before が.
あれ
あれ means that one over there in あれが欲しいです. It identifies a particular item that is not referred to as これ. Use it when selecting a different, clearly identifiable item and saying that you want it.
は
は marks the item as the topic in これは好きです and それは好きではありません. It presents the item first so the speaker can state a positive or negative preference about it. Use the pattern Xは好きです or Xは好きではありません when talking about whether an item is liked.
好き
好き indicates liking or being fond of an item in これは好きです. In それは好きではありません, the same word appears inside the polite negative expression for not liking the item. Use it after a topic marked by は to state a preference.
それ
それ means that or that item in それは好きではありません. It refers to an item already identifiable in the conversation and makes it the topic before the negative preference. Use it when the listener can understand which item is being discussed.
ではありません
ではありません is the complete polite negative expression in それは好きではありません, meaning that the speaker does not like it. In this construction, で links 好き to the predicate, は gives the negative expression its topic or contrastive shape, あり supplies the be element, ませ provides the polite negative ending base, and ん completes that negative ending. Reuse the complete pattern Xは好きではありません when politely saying that an item is not liked.