1. Give me five grapes from the bunch of grapes.

2. You should call the Internet connection company. Then you can get the Internet installed, but you should have your ailen card.

3. Interview two of your new friends and write down the information of the friends in the table on the page of the textbook.

(Would you check the sentences and correct errors, please? Thank you.)

In 2, do you mean "alien"? (spelling?)

In 3, I'd rephrase just a bit: "... and write down your friends' information in the table ..."

1. Give me five grapes from the bunch of grapes.

This sentence is correct. It is a request to receive five grapes from a bunch of grapes.

2. You should call the Internet connection company. Then you can get the Internet installed, but you should have your ailen card.
There is a typo in this sentence. "ailen" should be corrected to "alien". Additionally, it is unclear what is meant by "alien card". If you are referring to an identification card, it is more commonly called an "ID card" or "identification card". The corrected sentence would be:
"You should call the Internet connection company. Then you can get the Internet installed, but you should have your ID card."

3. Interview two of your new friends and write down the information of the friends in the table on the page of the textbook.
This sentence is correct. It instructs someone to interview two new friends and record their information in a table on a textbook page.