[Horsa]

Discourse analysis could be an analysis of any text, so it would include written texts, etc, while CA is a subset, looking at 2 or more people talking.

This means exactly what I said in my reply: that CA is included in DA.

I mean in discourse analysis we do not look at 2 or more people talking but in CA we do. am I right?

No, I am afraid not. DA covers everything including CA. CA is a specialist area within DA.

finally can we say that in both CA and DA we look at the followings:
1- how the data is processed ?
2- what is the purpose and goal of the data?

DA is the study of language in use - that is used for communication.
I deals with cohesive devices, address forms, how individual words such as articles or pronouns and how th choice of tenses affect the structure of the discourse. It also looks at adjacency pairs and relationships between utterances within the discourse being studied. Also turn-taking, how speakers change topics etc.

If you want to know more, there are a couple of reasonably priced books available.

Introducing Discourse Analysis by David Lunan from Penguin

Discourse by Guy Cook from OUP

Alternatively a basic explanation is available at wikipedia just follow the link below.

Discourse analysis - Wikipedia, the free encyclopedia