CORRECTION: 

You can only carry pre-approved things in this conference.  --*Correct sentence!~ ^^ 

They said, they can't redeem this gift card for cash. --*Correct sentence!~ ^^ 

This company have always been offering additional merchandise when the consumer buy their products, but it's useless.

Better say: This company has always offered additional stuff when customers purchase their products, however it is meaningless.

I hope he recommends a decent product this time. --*Correct sentence!~ ^^ 

The party was all set, half of the people who she invided didn't come.

Better say: The party was all set, however, half of the people she invited didn't show up. 

He can be in debt again after he pay precent debt off.

Better say: He may get indebted again after paying off the majority of his debt.

If you want to pass this gate, you need to have a pre-approved document.

Better say: To pass this gate, you must have a pre-approved document.

A lot of people give a gift card to someone for a birthday present.

Better say: Many people send gift cards to others as birthday presents.