Hi
Seblod's Conditionals are not what you want (if that is what you mean by Conditional)
In your search form, you can add the field 'author id' - I think it is called that. or maybe author name. Now, in the 'Live' area, select user, and then the id... or name, depending on what value you are checking. anyway, that is how to restrict lists to current user...
Same with Published and unpublished articles.
The field is 'Article State' (or Article States, can't remember right now)
For live value you can set it as publisher or unpublished. etc....
Also, to make the form more safe, so that users can NOT see unpublished, create a new field, same as 'Article State' and set defaultValue as 'whatever' ie 0. Then place it in clear position.... this way, the value will always be used in the search query , no matter what tricky ideas the user might have.