By its nature, dialogue is contrived. We don't want to write the way people really talk. Just read a court transcript sometime. Real speech is full of ums and ers, backtracking and repetition, and telling people things they already know. However, we do want to give the impression of how people really talk. So we make liberal use of sentence fragments and comma splices, idiomatic and clichéd phrases, as well as intentional misspellings that indicate region, ethnicity, or class.
When we write dialogue for non-humans or humans not of our time and place (hereafter collectively called "aliens," for simplicity's sake), we must surmount an additional challenge. We want our characters to "sound" alien or foreign, but we also want our readers to understand the dialogue without too much work.
Let's look at some examples of bad SF/fantasy dialogue. I made these up, but you can have fun and sharpen your "ear" for dialogue by finding similar examples. You sometimes can find problematic dialogue in professionally published work, but you're most likely to find it in e-zines that don't pay their authors. If you're in a writers' group, look for problem dialogue in the drafts submitted for critique. And, of course, take a hard look at the dialogue in your own work!
In his native tongue, which our narrator claims to understand well, Kneeling Elk is undoubtedly more fluent than he appears here. Fortunately, English is a flexible language that can, even in translation, capture cultural nuances. Thus, the fact that Kneeling Elk is "honored" rather than "pleased" or "happy" or just, like, "Hey, man! Whassup?" tells us something.
We have another opportunity with "many long time." "Many moons" and "many turnings of the sun" are clichéd, but let's say our characters are meeting next to a stream in the autumn. Then, to give us a sense of how his culture perceives the passage of time, we might have him say, "Have you seen many leaves float past?" Or a different cultural clue would be given by, "Have you had to eat alone?"
If this is all that Brzzzt says in this story, the Z approach may be okay. In a humorous story, it may even add something. However, if Brzzzt is a talkative giant fly, do we really want to read through lines of Zs followed by echoes in English? Brzzzt buzzes -- just tell me that she buzzes, or have us hear a buzzing fly-to-fly conversation going on in the background somewhere. Then give the rest to me in translation.
It's not unusual for authors attempting high fantasy to put high-falutin' words in their characters' mouths, in the mistaken notion that such dialogue will impart a majesty to their characters and setting.
"But Tolkien does it!" True: J.R.R. Tolkien does use such language, sparingly, when regal characters are in the most formal or grave of circumstances. And Tolkien had a background in linguistics and knew what he was doing. As a rule, don't try to write in the English of the Bible or of Shakespeare unless you can write it to that standard. And even then, don't overdo it.
That last advice -- don't overdo it -- is really the key to alien dialogue. We need to trust our readers to understand that, although they're reading the story in contemporary English, the characters are speaking something else. If concerned about whether our dialogue is over the top, a good question to ask ourselves is: If my story were set today in Mexico City, and my characters were sitting around after dinner discussing what to do next (in Spanish), would I be "enhancing" their dialogue as much?
C.J. Cherryh does an excellent job of conveying the sense of a different language, and the entire culture and social relationships that come with it, in her "atevi" novels, and she does so with a very light touch. A sprinkling of "untranslatable" words, variations of characters' names in more familiar or more formal forms, and the occasional shift to the impersonal "one" rather than "you" -- these combine to let us know the characters are speaking a very different language, without reducing readability.