Te-Form (3) - give & receive
Extends the common forms of あげる, くれる, and もらう, but what is received or given is now a verb, instead of a noun.
てあげる
Expresses that someone is doing or did something for someone else. The person that received the favor is followed by the に particle. Only for verbs.
Example
母にケーキを買ってあげた。 I bought a cake for my mother.
For casual language, てやる can be used.
てくれる
Used to ask a favor from someone or to say that something was done to the speaker. The person that received the favor (usually oneself and thus omitted) is followed by the に particle. Only for verbs.
Example
友達がギターを教えてくれる。 My friend will teach me the guitar.
てくれてありがとう
This form expresses gratitude for something that benefited the speaker. It is not used for something expected. Only for verbs.
Example
今日来てくれてありがとう！ Thank you for coming today!
てもらう
This form expresses gratitude for a favor that the recipient generally requested for, or where gratitude is the focus. Only for verbs.
Example
友達が手伝ってもらった。 My friend helped me (and I owe him / because I asked him and I am grateful)
てくれない・てもらえない
Used as a mean to ask for a favor like “would you, could you?“. Used in a similar form to じゃないか. Only for verbs.
Example
電気をつけてもらえないか。 Could you please turn on the lights?
電気をつけないでもらえないか。 Could you please turn off the light?