[susan53]

The problem here is that a lot of the sentences are unnatural rather than, or as well as, incorrect. Here's what we'd normally say :

1) I said that I would go with you. OK -this is correct
2) Let's go and play football tomorrow.
3)I know the man who/that owns the pink car.
4)That word means "tiger" in English. OK
5)I can see the red box (which is /that's) inside your room.
6)I saw your cousin at the airport.


1)I told you that that I would go with you.
2)I have an idea that we're going to play football tomorrow. ( = I think that we're going to ... etc)

4)I know the word in English which/that means "tiger".

Your problem here is that you're mixing up three different uses of the word "that". And they all have a completely different grammar. Check in a grammar book for :

1. That = demonstrative adjective or pronoun : Look at that car! Look at that!
2. That as relative pronoun in defining relative clauses : I read the book that you recommended.
3. That as subordinating conjunction : It's important that you remember to tell me./ He said that he would go.

I think one of the reasons you're confused about English is because you're trying to understand 101 different things all at the same time. I think you'll find it easier if you concentrate on one thing at a time.