Slowly getting to like K2 more as I find out what it can do!

But I would like to be able to change some of the "fixed" text in K2 ... e.g. the title Additional Info that heads up extra fields, the title "Children categories" that appears when showing a category list.

Do I do this by changing a language file? I did not see anything in the Parameters or Category details ...

Study up on K2 templating or overrides...Create one
Then search category.php category_item.php and item.php
You will find most of what your looking for in those files and can change it there.
There are also strings in the language file that can be changed to suit your needs as well