Can the word THAT be always left out?

Question

For instance: She said her father is ill, insread of: She said THAT her father is ill

Typing error: insread
Correction: Instead

I know this word can not be left out when it's a demostrative pronoun or adjetive

I mean when it's a conjunction or relative pronoun

Answer 1

No.

"She said THAT she went to the gym." = "She said she went to the gym."

But: "She went to THAT gym." cannot be "She went to gym."

When "that" is being used as a determinant (determines which one, just like an article) then it has to stay.

Answer 2

You can leave it out only sometimes. When you are referring to a specific thing by saying "that" you cannot leave it out Also you cannot leave it out if you are referring to a direction, for instance, She went that way. It has to be there to make sense. Oh by the way, what is your first language?

Answer 3

In that instance yes. But what about "Yes, that man did it"
You couldn't say "Yes, man did it" it would just be odd.