If there is no necessity of a database for my website, is it still a MUST to have mySQL for the WP in my local machine?
Without MySQL database, PHP, Apache and other PHP dependencies, Apche modules WordPress will not run. On local computer, a LAMP server is emulated or really used. There is basically no difference between localhost installation and server installation of WordPress software.
So, MySQL is must.
Only way to bypass MySQL usage of localhost is to use a cloud database as a service which provides an unique IP or FQDN - you can can use that MySQL database to install WordPress locally. However you will require active internet connection. Example of cloud database as a service is that of Rackspace Cloud. This is a high end setup, possibly you are not asking for this way.
At present I am working on a website which does not need a database.
All data of a WordPress software installation are stored on MySQL database. Only the images / uploads, extra plugins, themes are stored on wp-content/uploads folder.
Please install WordPress locally (on your own computer) to understand how WordPress software works.
If your need is a website with few webpages, it is possibly better to use handcoded HTML webpages instead of WordPress to build the website.