Android - How to extract .zip through ADB shell

Yes and no. As far as I'm aware, a typical Android install will not contain unzip. You can, however, install busybox for Android, which provides the unzip utility. Then a simple:

adb shell unzip /sdcard/archive.zip

Would do the trick. If you're rooted you can use a busybox installer from the Market like Stericson's. If you're not rooted then you should be able to manually push a busybox binary (one here on Github, for example; click "raw" to download it) to somewhere like /data/local and then invoke it. It should be something like:

adb push /path/to/busybox-android /data/local/busybox
adb shell chmod 0755 /data/local/busybox #Make it executable
adb shell /data/local/busybox unzip /sdcard/archive.zip

Alternatively, many file managers will unzip files for you. I personally use File Expert but there are a lot of others. Usually you just need to long press on the archive and it will present an "extract" option or similar.