macOS Mojave Installation I have downloaded macOS Mojave from some other website due to Mac App Store download problem. So now I have to boot the installation file, to do so the help box of the website says I have to press and hold Option key on system restart.

Does this action erase my whole mac hard disk?
No, holding option on restart simply lets you boot off a different device. It doesn't erase anything. But having said that, downloading MacOS updates from anywhere except Apple is very risky, and I wouldn't recommend it. Booting from a different device won't erase your hard disk, but running a rogue installer could.