Cats loves to hide in the trees.
Ok!

Whe I saw a cat that had no fur, I was speechless.
Watch your spelling! You mean {when}?
When I saw a cat that had no fur, I was speechless.

Liger is bigger than a cat.
{Liger} is a countable noun. Add an article here.
A liger is bigger than a cat.

Cats like to chase bird wher the birds are sound.
{Bird} should be in a plural form. Also watch your spelling.
{Sound} is a noun or a linking verb.
Cats like to chase birds when the birds are making sound.

hobby (n) 爱好
I have many hobby.
{Hobby} is a countable noun. Use plural form here.
I have many hobbies.

They have many hobby.
The same problem mentioned above.
They have many hobbies.

Everyone have hobby.
{Everyone} is the third person singular, so we use {has} here.
Everyone has hobbies.

conversation (n) 交谈
I am in a conversation.
I hate to be in a conversation.
Ok!