No option on App Store to update High Sierra to Mojave Well, I have MacBook Air (early 2014) with High Sierra 10.13.6 OS and there is no option in AppStore to update to Mojave. I tried downloading directly from App Store and it stoped after every 500-800 MB, although it resumed from where it was stopped. but, after 100% download nothing happened, it didn't ask me to restart neither any error. So, is there any problem or is it not compatible with my machine.?
Based on your post, your MacBook should be compatible with the Mojave update.


Once the App Store app finishes downloading and installing you should see a installer in the Launchpad (it should automatically open, otherwise try double clicking on it to manually start the installer).
 
If this doesn't work out you might want to look at making a bootable USB installer, and proceed with the installation after booting from the USB stick. See here (Apple Support Documentation)