这个国的寿命是真漂亮!

I don’t understand the sentence. I'm guessing you meant "This country has a high life expectancy!"? In this case, you'd say "这个国家的人寿命真长！"

一个人平均住人均寿命是97岁。

I think "人均寿命" is a more advanced vocabulary so you might not know this, but this is the way you express the average life span of a person. :)

信已经就寄到了吗?

你给我过目啊!

The sentence is correct but with the exclamation mark it sounds like you're giving an order and sounds kind of rude hahah. So be careful when you use this in real life!

周杰伦唱得真优好啊!

"优" is technically correct, but usually when we comment on someone's singing we'd just use "好" to describe it.

你有没有处惩罚过你的孩子啊?

"惩罚" sounds more natural :)

你会帮我准备好复习历史的考试吗?

I get what you're trying to say here, but I think in Chinese, it's more natural to ask someone to help you revise ("复习") the exam instead of asking them to help you get ready for it.
Also, when you want to specify the subject of the exam, you simply add it in front of the word 考试. It works as a noun phrase, so you don't need to add "的".
For example,
中文考试 Chinese exam

不然这里就会很闷热。