Hello Everyone,
After checking some forum discussion, finally I've managed to check domain availabilty from external/home page
Procedure:
First go to (for edit) /{blesta-install-directory}/config/blesta.php & search following line:
Configure::set("Blesta.csrf_bypass",array());
Now replace that line with following code (No need to disable automatic csrf token protection for whole site):
Now configure your external/home page domain checker form, here is my code:
Thanks everyone