When to use こと　and よう　？

こにちわ！！When do we use ことandよう ? I've been reading examples of them but haven't been able to figure its real usage in japanese conversation. could you guys please explain it in detail and give example of them ? I'll be looking forward to your answer.
Ouu and here's what I currently think bout how to use them:
時計を買うことかになったよ。
先生は難しい宿題を私にさせることはなったよ
Are these two sentences grammartically correct?
ありがとうございます！！

時計を買うことになったよ (か is unnecessary)
先生は難しい宿題を私にさせることになったよ

ことになった and ようになった are both set phrase.
ことになった: a thing/event/plan was settled
ようになった: became (a state/habit)
e.g.
彼女とすしを食べることになった。
A plan I will eat sushi with her is settled. = I will eat sushi with her.
最近すしを食べるようになった。
(I used to not eat sushi, but) I eat sushi nowadays.

こと and よう have so many meanings other than this set phrase. It's impossible to explain all the usages.