If you talk about a musical group reaching their zenith, you're talking about the time when they're the most successful that they've ever been. If you talk about a game or a trend reaching its zenith, again, you're talking about the time when it's gotten really cool, with lots and lots of people playing that game or following that trend. And when a product is at its zenith, that's when the most people are buying it.
You might look at the word "zenith" and want to say it with a short E, like this: "zenn-ith." That's fine if you want to say it that way. Many people do. I'll keep saying it "zenith," which is the regular American way to say it. Here's a fact that might help you remember the regular pronunciation: "zenith" comes from Arabic, and so does the word "zero." And it's pretty easy to say "zero" with a long E, right?
"Zenith" is a lovely word. It's a common word, but it's not extremely common. So, you should pick the word "zenith" when you want to add beauty to your sentence, and when you want to compare something to the sun, or to a star, or to a ball thrown through air: something that seems to be floating high above us. If that's not what you're trying to do, then you should pick a more common word instead, like "top," "peak," or "height."