Hello,
the reason can really be, there exist either another record with same non-sef parameters, i.e.
"index.php?option=com_content&id=568&layout=default&view=category" or there already exists "/theatre" SEF link;
this reason is most probable and JoomSEF prevents you to create a duplicate

Another reason could be that the SQL query for storing the information fail from some reason. Try to turn on error reporting and debugging to maximum level and see if there does not occur any error.

I have SEF link with the name theatre.
How can I delete the old one?
Or how can I use the same SEF url from Joomla to the JoomSEF?

The SEF URL should be unique. When it is not, it leads to problems when JoomSEF does not know, what URL to use (the original).

The solution would be following:
1. delete the current /theatre SEF link (or better rename it to something else)
2. edit (rename) the link you want to be /theatre

In case you would delete the first link (not rename), it may happen it will be recreated in JoomSEF. Then you would have 2 /theatre links stored, which could cause the problem as mentioned above. In that case, again, you should rename one of them to something else OR use the "activate" button in JoomSEF URL Manager and make the correct link "active".

I make the first choice (1. delete the current /theatre SEF link (or better rename it to something else)) and I rename the existing SEF with somethink else.
When I am on the JoomSEF URL Manager and on the editing page i have the same problem. I editing one url with the whole fields( New SEF URL, Title, Meta Descrition:, Meta Keywords:, Meta Content-Language:, Meta Robots: ) and after saving the current url is not saving.

How can I solve it and make the JoomSEF working.

I install the JoomSEF to another Joomal 1.5.15 and the JoomSEF URL Manager where empty. I had to create new url's.
So, on my Joomla site that I have a problem is the right way to delete the whole existing url's?
And create new url's.