I'm lovinge to study English.

I'm working forteaching elementalry school students.

"working for" elementary school students means the elementary school students are your bosses. You can also say "I'm working at an elementary school."

I had a lesson aton Saturday school today.

But this day is athe first day of the new year so we held a Karuta tournament.

Especially, for kids, it's easy to learn a lot of new words through this game.

The winner got five pieces of candies.

Depending on which region's English you are learning, you can also use candy for plural (I think Americans tend to just say candy)

The second one got four pieces of candies.

The third one got three pieces of candies.

But we teachers got many pieces of candies in the teachers' room after the tournament.

It's a top secret . (from kids.)

From kids is implied. It's more natural to leave it out.

I'm loving toe studying English.

I'm working forwith elementalry school students.

Saying "for" makes it sound like they're your boss :)

Another translation of your original sentence might be something like "I work at an elementary school"

I had a lesson at Saturday school today.

But this day is athe first day of the new year so we held a Karuta tournament.

Especially, for kids it is easy to learn a lot of words through this game.

And also it'sit's also fun to play.

The sSecond onplace got four candies.

The third onird place got three candies.

But wthe teachers got many candies in the teachers room after the tournament.

"teacher's lounge" or "staff room" are some other words for that room in the US.

It's a top secret from the kids.

I'm loving to studying English.

I had a lesson at Saturday school today.

But this day is athe first day of the new year so we held a Karuta tournament.

Especially, for kids it's easy to learn a lot of words through this game.

AndIt's also it's fun to play.

Sounds more natural

Others got one candy as a participant reward.

I'm loving toe studying English.

Or, "I love to study English"

I'm working for teach elementalry school students.

Or, "I work at an elementary school."
If you say "I work for x", x is usually your company or boss.

But this oday is athe first day of the new year so we held a Karuta tournament.

Especially, for kids itFor kids it's especially easy to learn a lot of words through this game.

The sSecond onplace got four candies.

The third onird place got three candies.

Others got one candy asfor being a participant.

But we teachers got many candies in the teachers' room after the tournament.

It's a topbig secret from the kids.

I don't know why, but to me, "it's top secret from somebody" sounds a little strange. If you want to use "from", I would not use "top."

I'm loving toe studying English.

I'm working for an elementalry school students.

Work for [someone] means that [someone] is the one who is employing you

I had a lesson at school on Saturday school today.

But this day is athe first day of the new year so we held a Karuta tournament.

There's only one first day of the new year, so it's better to use "the"

Especially, for kids, it is easy to learn a lot of words through this game.

The second onplace got four candies.

The third onplace got three candies.

Others got one candy as afor participanting.

But we teachers got many candies in the teachers' room after the tournament.

It's a top secret from the kids / This is top secret information from the kids.

I think it sounds more natural to use "top secret" as an adjective rather than a noun.

I'm loving to studying English.

「I love studying English」とも言えます。

I'm working for an elementalry school students.

「I work at an elementary school」とも言えます。

I had a lesson at Saturday schoollesson today.

日本語では「サタデースクール」と言いますが、英語では「Sunday school」という表現が一般的です。ただし、「Sunday school」は通常、宗教教育を指すことが多いです。土曜日のレッスンを表す際には、別の表現の方が自然かもしれません。

But this oday is athe first day of the new year so we held a Karuta tournament.

Especially, for kids, it is easy to learn a lot of words through this game.

The second onerunner up got four candies.

「Runner up」とは、2位の人を示します。

The person in third onplace got three candies.

3位の人を示す特別な表現はありませんが...。^^;

OthersEveryone else got one candy as afor paticipanting.

But we teachers got many candies in the teachers room' lounge after the tournament.

It's a top secret from the kids.