Damicci said:
「～くれる」の使用をあまり分かんない。 でも、誰かが別人に好意として何かをしたら、その時は「～くれる」を使うでしょう？ そして、「～くて」は「～くれる」の活用ですか？ 使用を分かんないけど、その用語をたくさん聞きます。
In English one use noun when talking about the concept or something abstract, but in Japanese one tends to use verb or clause.
I don't understand the usage of ～くれる well.
but in Japanese
「～くれる」の使い方があまりよくわからない。
(instead of "usage" we say "how to use")
Likewise 使用はわかんないけど → 使い方はわかんないけど
Now about 「くれる」.
It means someone gives something to another, viewing closer to the receiving side.
When it is combined with another verb, it implies some kind of favour is being done. This is what you mentioned 好意 in your post, I think.
「もらう」 is similar to 「くれる」, but means "to get". Implication of gratitude is less than 「くれる」.
「あげる」 is about the same action, but viewing from the giving side.
Sometimes it implies friendliness, but it also could sound patronizing.
ともだちが父に本を送った。
(A friend of mine sent a book to my father.)
is just a statement of a fact, while
ともだちが父に本を送ってくれた。
shows that the speaker feels gratitude/appreciation for what the friend did.
「～くれる」 is used with te-form of verb.
「～くて」 is something different.
When used with i-adjective, it states the reason.
悲（かな）しくて涙（なみだ）が出（で）た。
also list up more than two
大きくて青い車
for example.
したい (to want to do____) conjugates like i-adjective, so
「～(し)たくて」 is often heard, like 聴きたくて, 勉強したくて, etc.