In vim I can invoke ':make', which starts make, and if there are errors, it opens the file at the line where the error was. Is there something similar in kate? I've found a 'Focus Terminal' command, but it just opens a terminal, and I am specifically looking for the feature where the text editor goes to the lines where there are errors.
As far as I know, the answer is NO.
As you already found out, there is a terminal plug-in, from which you can invoke the make (and that is what I do).
Aparently, they added the build plugin for kate.