i guess we have to know a bit about the word order in czech. if we really mean "a terrorist killed himself", we would switch it up as "zabil se terorista", or would be stuck sounding rather odd saying "TERORISTA se zabil" to make up with stress what we messed up in the word order. it is called topic/focus, an important area of linguistics. but it is not realistic to expect people to pick it up from a duo course, so i will make sure to add the questionable alternative if it is still missing.
I think that you don't have to know who he was, just the existence of a terrorist should be already known.
But the sentence in question would be a strange introduction of his existence. And in a headline I would expect "the".
But I am curious for an answer from a better knowledgable person myself.
"And in a headline I would expect 'the'".
Actually, in English language newspapers, headlines usually do not use either the definite or the indefinite article, and the headlines are usually written in the present tense.
So the standard headline here would be: "Terrorist kills self" or "Terrorist kills himself". (The "himself" would be used only if the longer word were needed to fill out the line.)