Childred have their balloons in classA class of children are each given a balloon.

"Children" as the subject makes this sentence sound very general, like you are talking about all children. "Children often get very bored in class."

"their balloons" makes it seem like it is obvious that a child would have a balloon, like you are assuming the reader knows exactly what balloon you mean. You might say "A class of children have their pens", but you would probably not say "A class of children have their bottles of vodka" - it is new information that a child would have a bottle of vodka, so you'd want to introduce it somehow rather than just assume the reader understands.

Maybe in Korea balloons are standard equipment? :)

Following their teacher's guideinstructions, they write their names on their balloons and throw ithem away.

"guide" as a noun doesn't work very well here. You could say "following their teacher's guidance" or "Their teacher guides them to", but "instructions" is most natural for me.

Singular/plural is difficult in a sentence like this. "They" here are acting as a plural group, so they write on their balloons and throw them - multiple children, multiple balloons. But you could say "each of them writes their name on their balloon and throws it away".

The teacher asks them to find their own balloon forin five minutes.

I don't know how English grammar describes this, but "find" is a verb that has a sort of perfective aspect, it implies the completion of the action. You *successfully* found the thing. It focuses on the instant of success - so you can't "find [something] for [a duration]". I suggest changing five minutes from a duration to a time limit, but you could also just "search for their own balloon for five minutes", "look for", or "try to find".

The childredn try to find ithem but it is very difficult.

Some kids argue for better position to findand fight about others being in their way.

Probably the most natural way to say this.

After five minutes, only a small number of children success in findinghave been successful.

Unnecessary to say what they've succeeded at, because we know what the task is. But you do need a verb!

The teacher gives another instruction, that they should picking up a balloon nearby and handling it over to its owner.

It would be "handing" not "handling". But constructing this with the gerund is quite unnatural.

Then everyone has their balloons forafter a short time.

"has their balloons for a short time" - duration. They have their balloons, a short time passes, and then they no longer have them.

"If you findseek your own happiness, it will be very hard to havefind.

Again the perfective thing - finding is the success at the end of seeking/searching for. So if you find your own happiness then you are happy!