I just bought a Nikon D7100, with the basic kit lens 18-105mm. I was wondering, if I can capture stars or milky way with it. Will the answer to this question work for me? As it says 24mm on f/2. Also how do I protect my LCD, as it doesn't have any protective cap, as my previous D90.
You will need to use a smaller aperture (somewhere around f/4.5-5.6, slightly closed down fro the maximum aperture) because your lens isn't as fast, but you can compensate somewhat by raising the ISO a bit as well (the D7100 ought to be okay-ish at ISO 3200). 18mm is also not quite as wide on DX as 24mm on full frame, so you won't get as much of the sky and star trails will be more prominent at any given shutter speed/exposure duration. It won't be as "clean" a picture as a faster lens on a full-frame camera, but it shouldn't be too terrible either, provided that you aren't trying to capture the faintest details in the night sky.
You don't need a screen protector for your camera. Unlike much older models, the LCD screen on the D7100 is made of Gorilla Glass (like the screen on an iPhone), so scratching in normal use shouldn't be an issue. If you're not confident without a protector, there are a number of third-party suppliers. Note that most of them will attach in place of the viewfinder eye cup because the D7100's screen is flush with the camera back and there are no attachment points for a cover.
Getting good or interesting results shooting the night sky involves a good deal of experimentation. You can't shoot at f2 (your lens isn't that fast) so you'll need a longer shutter speed and/or a higher ISO. (Try doubling or even quadrupling the shutter and/or ISO.) Finding somewhere really dark to shoot will make a very big difference in the result, too. You didn't mention it, but note that you'll need a tripod to hold the camera steady enough.
In other words, yes, you can get good results with your equipment. And, just like the rest of us, you'll need to do some experimentation to get the results you're after.