かな as "I wonder"

かな can be added to the end of a sentence to mark a question or remark that's addressed to either oneself, or those in the speaker's current group. It's often translated as "I wonder..."

春休みは何をしようかなあ。
I wonder what I should do for spring break.

シュウは誰か好きかな。
I wonder if Shuu likes someone.

このアパート、よさそうだけど、ちょっと高すぎるかな。
This apartment seems nice, but I wonder if it's too expensive.

今日アヤトとライトは学校に行ったかな。
I wonder if Ayato and Laito went to school today.

ようにする

A plain, non-past verb + ようにする can be used to indicate "one's conscious effort to do something for some purpose." It's often used to describe habitual actions, although it can also reference a single action or event. It can be translated as "make an effort to do [verb]" or "try one's best to do [verb]."

先生今日は授業に遅れてすみませんでした。明日からもっと早く家を出るようにします。
Sensei, I'm sorry I was late for class today. Starting tomorrow I'll do my best to leave home earlier.

仕事に間に合うようにしたほうがいいよ。
You'd better make an effort to be on time for work.

環境のために、紙をリサイクルするようにしてください。
Please make an effort to recycle paper for the sake of the environment.

日本語のクラスを取ったら、各テストに勉強するようにするよ。
If I take a Japanese class, I'll do my best to study for each test.

くれる and もらえる

I've reviewed this before in a Genki chapter, but reviewing grammar never hurts. A verb in the て form plus くれる, もらえる, くれない, or もらえない translates to something like "could you" or "would you", asking for a favor. It's used with rising intonation to make a request during casual conversation.

初めてケーキを焼いたんだけど、ちょっと食べてみてくれる？
I baked a cake for the first time, so could you try a little for me?

ライト、かぎを取ってもらえない？
Laito, could you get my keys for me?

もし時間があったら、明日空港に迎えに来てもらえない？
If you have time tomorrow, could you pick me up at the airport?

トキにえさをやりてくれない？
Could you feed Toki for me?

ように頼む / 言う

The phrase ように頼む / 言う is used to indirectly quote a request or command that was made. It's likely evident from the verbs themselves, but ように頼む translates more naturally as "to ask someone to [verb]" while ように言う is more like "to tell someone to [verb]."

The structure used here is generally [present tense verb] + ように頼む / 言う. An affirmative ように頼む request is often preceded by a verb in the てくれる form. Negative requests or commands simply use the verb in the ない form.

先生は学生に「漢字を覚えなさい」と言いました。
The teacher told the students, "Memorize the kanji."

先生は学生に漢字を覚えるように言いました。
The teacher told the students to memorize the kanji.

These examples should provide a better understanding of what this phrase actually does. Rather than directly quoting what the teacher said, we're giving a secondhand account (essentially paraphrasing) of what he told them.

パーティーをしていたら、隣のアパートの人に静かにするように言われてしまいました。
When we had the party, we were told by the people in the next apartment to be quiet.

アヤトに買い物に行くならきれいなドレスを買ってくれるように頼んだ。
I asked Ayato to buy me a beautiful dress if he goes shopping.

ウェイターにデザートメニューを持って来てくれるように頼もうか？
How about we ask the waiter to bring over the dessert menu?

スバルは学校の後に家に帰るように言われてた。
I was told by Subaru to come home after school.

ことになった

A non-past verb + ことになった can be used to express that "a situation has changed due to some external force (e.g., a decision was made by someone other than the speaker)." It's important to remember that the speaker did not make the decision that caused the situation to change. Let's compare a couple other similar grammar points to distinguish them.

ことにする - The speaker or subject made a decision to do something.

ことになっている - Something has been decided and the result of that decision is still in effect.

 ことになった - Something was decided in general, and perhaps associated with a single action.

日本にあるオフィスで働くことになったので、日本に引っ越すことになりました。
It's been decided that I'm going to move to Japan since I'll be working at the office there.

来学期田中先生は英語の文学を教えることになった。
It turns out that Tanaka-sensei will teach English literature next semester.

環境をよくするため、来月からリサイクルキャンペーンをすることになった。
The help improve the environment, it's been decided that we'll have a recycling campaign next month.

来週化学のクラスに微生物を勉強することになった。
It turns out that we're going to study microorganisms in science class next week.

More on ていく and てくる

Previously I learned about how ていく and てくる are used to indicate the direction of movement with a verb, or indicate a sequence of actions. The following are examples of each:

図書館で本を借りて来る。
I'll go to the library to borrow some books (and will come back).

買い物する前に、銀行でお金をおそして行く。
Before shopping, I'll get some cash from the bank (and then go shopping).

But ていく and てくる can also be used as helper verbs to indicate the temporal direction of something from the speaker's viewpoint. てくる can indicate that an action or process began in the past and is continuing in the present, or that something has begun to take place.

日本語の文法が面白くなってきました。
I'm beginning to find Japanese grammar interesting.
It's gotten to where I find Japanese grammar interesting.

I did two translations there, one from Tobira and one of my own, to give something a bit more literal that pairs with くる's meaning. Thinking of it as "it's gotten to where", "it's come to where", or "it has become" fit well here because they're talking about something that's begun to take place and yet will still continue.

ていく, on the other hand, can be used to indicate that an action or state will continue from the present and into the future.

今学期は一週間に10ずつ新しい漢字を勉強していきます。
This term we are going to study ten new kanji a week.

It's a little harder to offer an alternate translation here, but ていく can often be thought of as "continue" or "to go on [verb]-ing."

最近、ちょっと暖かくなってきました。
Lately it's beginning to get a little warm.

技術が発達したために、生活がとても便利になってきた。
Since technology has developed, life's gotten to where it's really convenient.

この地方は北にあるので、夏は午前4時前に空が明るくなってくる。
Since this area is in the north, in the summer the sky is beginning to get bright before 4 AM.

これから、もっと暖かくなっていきます。
From now on it'll start to get warmer.

ゴールデンレトリバーは大型の犬だから、もっと大きくなっていきますよ。
Since golden retrievers are a large type of dog, they'll continue to get bigger.

ロボットがもっと人々の生活を助けるようになっていくだろう。
Robots will continue to help out more with more with people's daily lives.

をしている For Descriptions

The pattern [Noun 1は + Adjective + Noun 2 + をしている] is used to describe a feature of someone or something. It generally focuses on a certain attribute, like describing a person's eyes, an animal's ears, etc. That structure looks a bit convoluted, so let me give an example.

馬は足が長い。
馬は長い足をしている。

These sentences are synonymous. Both of them are stating that horses have long legs, just with slightly different grammar. Thus, the をしている portion is probably best translated as "have."

One last thing is that している often becomes した when the phrase modifies a noun.

このオペラ歌手は、本当にきれいな声をしていますね。
This opera singer really has a beautiful voice.

兄の娘は大きい耳をしてるよね。
My brother's daughter has huge ears.

フレンチブルドッグは短い足をした犬だ。それに、面白い顔をしている。
French bulldogs are dogs that have short legs. They also have funny faces.

今日はスバルに会って、すごくきれいなくちびるをしてるんわね。
I met Subaru today, and he has such pretty lips.