In the future - I suggest you simply add to the thread you already started so that others might benefit from the Q&A.
1. How to change this text?
It depends on the template - which one are you using? If your template does not set the value of these links in the admin panel, they are most likely hard coded in your template's index.tpl file.
2. How to change this text?
I do not use that plugin, so I am not sure, and it looks like you have tried to find the source of this text in your other thread. Need to pass on this one - hopefully someone else has an answer.
3. How to create a header with background image?
A background image for the categories title?????
4. I want first 16 and then april. (16 April: TITLE)
Several possibilities here. Your screenshot looks like it might be one of the Andreas derivitives. If so, using Andreas08 as an example, the place to change that is in entries.tpl, specifically: {$entry.timestamp|@formatTime:DATE_FORMAT_ENTRY_ANDREAS}. So we can see that the author created a variable (DATE_FORMAT_ENTRY_ANDREAS) to hold the date format (although, they did not have to). In the corresponding language file, I found the variable defined here: @define('DATE_FORMAT_ENTRY_ANDREAS', '%b %e:');. Interpretation of that is : %b - abbreviated month name according to the current locale, followed by a space, followed by %e - day of the month as a decimal number, a single digit is preceded by a space (range 1 to 31). You can simply swith the order of %b and %e if that is all you want to change. If you want to change more than that, here is a complete list of the available date format codes:
http://smarty.php.net/manual/en/languag ... format.php
Also - those codes could have been provided directly to the entries.tpl, rather than defining them in a separate language file (ie {$entry.timestamp|@formatTime:"%e %b"}
If your site is live anywhere, it is often helpful to post a URL so people can see it in action.