In order for me to ask a higher quality question, I need to know, do constructed languages need to have their own letters, words, & sounds?
No, a conlang does not need any of it. You can construct a language based on gestures (a sign language) or on whistles, or on other signals transporting information. You can construct a Pasigraphy, i.e., a written-only language.
But for a more conventional design that meets our intuition of language, you will probably use sounds and words, and letters to write the language. It is up to your creativity to come up with original sounds and letters, but there is definetely no need to do so. Many conlang designs rely on sounds (and complete phonologies) that occur in natural languages, and use usual letters (mostly Latin, but also Cyrillic or other existing writing systems like Runes) for writing. The words of a conlang are most often original but I even can imagine a conlang without original words: Draw existing words for natural languages in an eclectic way or create a conlang closely based on a natural language or a group of natural languages. The vocabulary of IALA Interlingua is hardly original.
As has already been said, the answer is, generally no. However, I’d like to look into it a bit deeper:
Many (most?) constructed languages are written with the Latin script, i.e. what I’m using right now to write this answer. However, many conlangers find the base set of 26 characters it provides too restrictive, and will make use of things like diacritics (áèñħ…), special characters used in some languages or the IPA (ŋß…) or letters from other alphabets (εφϑ…). This is a choice, and by no means a necessity. Some conlangers, in particular those creating languages for a constructed world, also like to invent entire writing systems and consider the representation with the Latin script (“romanisation”) merely a tool for easy representation online. Again, this is optional, but depending on your goals might be a good idea. It would not make sense to create a new writing system for an auxiliary language though, for example.
There’s three ways one might interpret this question:
Do I have to make my words sound different (from English / any other language)? Certainly not: auxiliary languages often take heavy inspiration from existing languages, as familiarity makes it easier to learn a language. Similarly, if you want to toy around with grammar but don’t really care about the actual outcome, you might as well just use placeholder words taken straight from English and focus on what you really care about.
Do I have to make words which mean different things than the words in English/any other language? Here I am inclined to say yes. If you simply copy an English dictionary and replace all the words by other sounding words, then you’ve created what is called a relex. Whether relexes are considered conlangs or not is up for debate, in my eyes they are ciphers. However, there’s layers upon layers to this - is a conlang still a relex if you copy the lexicon but use completely different grammar? Perhaps not, but it’s not as interesting as if you also made a custom lexicon. In fact, I’d go so far as to say that doing so takes away most of what makes a conlang unique.
Do I have to follow the idea of having sentences broken down into words? Absolutely not: it’s actually surprisingly hard (read: an unsolved problem) to define the concept of a word in a way that works for every language. Look into the (just as loosely defined) concept of polysynthesis if you’re intrigued.
Language doesn’t have to rely on sound. There’s sign languages as a primary counterexample that also shows up “in real life”, and on top of that, graphical (written only), touch based and many other kinds of languages have been created.
But let’s assume you’re going to be making a spoken language. Two questions:
Do I have to make new sounds? Well… no. There’s only so many sounds our mouths can make and most of them already occur in some language (and those that don’t, e.g. smacking ones teeth together don’t occur for good reasons), so it’s rather hard to even make new sounds. But if you’re making a language meant for aliens/sapient animals/whatever nonhuman you can come up with, then maybe you might want to. But many conlangers don’t bother, as it is really hard.
Do I have to make a new sound system or can I just use the sounds of English/other language? Same point as with the words above: You don’t have to, and if your goal is to focus on other parts of the conlang you might as well ignore it, but if your goal is to make a good, interesting and unique conlang, then… yea you should.
In short, what you do and don’t do depends entirely on your design goals. If you wanna toy with a particular grammar concept, then focus on the essentials. If you wanna make the new big international auxlang then keep things familiar to the target audience. If you want to make a natural looking conlang, then go all in and be creative.
Yes -- after a fashion.
The main issue I have with your question lies in the specific terms used: words, letters & sounds.
So far, the answers have gotten around these things by pointing out whistle or sign languages. And I agree: technically speaking, in a sign language, there are no words and certainly no sounds.
The reason the answer is actually yes, I contend, is because I am sure what you actually mean by "words" is "discrete meaning carrying units of language" and by "sounds" & "letters" you probably mean "some way to convey said meaning through an interpersonal medium of communication".
When taken at the broader level, of course, language has to have "meaning carrying units" and it has to have "medium of communication". Else, language ceases to have meaning.
I would say that yes, ever invented language must have "words" (whether those words are spoken, signed, thought or written) as tokens of meaningful communication; and they must have "sounds" (whether spoken by mouth through the air or sent via radio waves between antennae) as a native & non-technological way of conveying meaning.
"Letters" indicate a specifically technological advancement to communication via language. An invented language's culture does not need to be that advanced. And even if it were, it would not need "its own" letters. It could borrow either someone else's writing system; for example the way Persian borrowed Arabic writing. Even though Persians had been writing for centuries already.