can I backup my macbook air to a wd easystore external hard drive?

Since most drives are formatted for Windows, make sure you format it for Mac (Mac OS Extended) and erase whatever software is on it during that process. External drives do not need any software or app to be able to function. The website for yours does mention that it needs reformatting; it also mentions that it contains backup software and that it needs to be "installed". Neither is necessary or recommended on a Mac. Simply plug it in, use Disk Utility to erase and format it, and you're ready to go, especially if you will be using Time Machine.

Sure.

Back up your Mac with Time Machine - Apple Support