He attends a soccer game.
Ok!

They went to Mc Donald.
Ok!

We write a letter.
Ok!

She turns down him.
{Him} is a personal pronoun that should be placed between {turn} and {down}.
She turns him down.

My rabbit admire carrot.
{ My rabbit } is the third person singular, so please add -s at the end of {admire}.
{Carrot} is a countable noun. Use plural form here.
My rabbit admires carrots.

He despises soccer.
{Soccer} is a countable noun. Use plural form here.
He despises soccer.

His cat jumps at his home.
We always say {at home} or {in one’s home}.
His cat jumps at home.
His cat jumps in his home.

They cherish basketballs.
Ok!

I protect my cat.
Ok!

We attend a school.
Ok!