I have been around a few JWs in my life, and I can confirm that JW's do indeed believe that Jehovah (God) killed the firstborn of Egypt. It is written that way in their preferred translation, the New World Translation (NWT)... which, by the way, is a pretty decent translation, that at least makes an honest attempt to translate the best available texts correctly. It's not perfect, and its almost literal (at times) translation leads to some perplexing passages.
JWs dislike the use of the phrase "The Lord" and "God" as they perceive them to be ambiguous. They don't believe in the Trinity, although they do believe that Jesus is second only to Jehovah (God). They use "Jehovah" as the name of the Supreme Being (God), which is technically quite accurate. There is really nothing magical about the word "Jehovah" or "Yahweh" (which are the same word, when translating ancient Hebrew). It's consonants only, and it literally translates as "Y or J, H, V or W, H". So... you can pick from YHWH (Yahweh), JHVH (Jehovah), YHVH, or JHWH. Everybody is just taking their best guess on that choice. It would be nice to know how everyone pronounced God's name when Moses freed the slaves, but I don't think it's gonna happen.
At any rate, the Hebrew word denoted by those 4 letters means (depending on which scholar you ask): "I Am" or "I Shall Be" or "I Shall Prove to Be."
I've read and made my very best effort to translate the oldest texts that I have access to, and compare them. In those texts, it appears that Moses is the first person recorded to have asked God, basically, "What is your name?" The texts seem to indicate that God was either taken aback by that question, or simply had no way to answer it in a way that humans could understand. So God answered, "I am." That's the best he could do without just giving a ridiculous answer like "Bob."
It's worth noting that Moses is the only person in the pre-Jesus texts of the Abrahamic religions that ever "talked back" to God or questioned God, and got away with it. The indication in those texts is that God respected Moses when he challenged God, because Moses had valid points and presented them in a shrewd manner. Personally, I think that Moses is the only pure human (in other words, not including Jesus, Mohammed, or other humans perceived as "divine")... Moses is the only pure human in the Abrahamic scriptures that God ever found to be worthy of his conversation.
Abraham, David, Solomon... They all had their virtues... But, without trying to sound sacrilegious, Moses is the ONLY human who ever threw the "bulls**t flag" at God, and made God think about it.
A little off-topic, but still relevant, I think. I apologize for the ramble.
I just realized that I never answered the original question.
Of course, as with any answer regarding any religious questions, these are my opinions and interpretations based on the information available to me.
Did God kill the firstborn of Egypt?
It depends upon who is answering the question. As mentioned, the NWT, the JW's preferred translation -- and many other translations -- state quite clearly that God did kill them. However, the definitive answer is a little harder to come by and depends upon which texts you consider valid and who is doing the translating.
Many Abrahamic texts indicate an "insulation" between God and killing. In many belief systems, God -- the Creator -- does not kill that which he has created. Depending on the beliefs of a certain religion, this could indicate that God is capable of error, by creating something that was a "mistake" and now must be destroyed. Obviously, the concept of a God who makes mistakes does not "fly" in many religions. Another philosophy is that God could never kill a living thing. His purpose is to create, and killing anything, directly, would make that purpose meaningless.
It is this second philosophy that leads to a theory proposed by many religions.
In some texts, God employs an "Angel of Death", "Destroying Angel", or "Destroyer." It is usually presumed that this Angel is a very high-ranking angel that reports directly to God, and is the ONLY Angel tasked with the killing of God's creation. The Destroyer is always depicted as having NO free will. The concept is that God could not bear for anyone to have to kill by choice. This does not mean, however, that the Destroyer does not feel or have independent thought. It just means that he must execute the law completely and literally, and obey all of God's commands. In many (not all) texts, it does not appear that the Destroyer is responsible for death by old age, random occurrences, or by people killing other people.
At any rate, before I write a Novel here, many religions argue that the Destroyer, commanded by God, took the lives in Egypt that night. In our human justice system, we might say that that makes God "just as guilty" as if he had done the killing himself. But in the context of many religious belief systems, that is not exactly the case.