Template for front page (latest posts)

whether a template can be provided for index.php?

There’s no built-in capability for selecting a custom template for archives.

How can i provide option for full width, sidebarleft& sidebarright options for index.php?

You can add a generic Customizer control with options for which template to use for archives, then inside index.php you would just check the saved value of that control with get_theme_mod() and change the template accordingly, or include another template file, for example:

switch ( get_theme_mod( 'layout' ) ) {
    case 'fullwidth':
        get_template_part( 'index', 'fullwidth' );
        break;
    case 'sidebarleft':
        get_template_part( 'index', 'sidebarleft' );
        break;
    case 'sidebarright':
        get_template_part( 'index', 'sidebarright' );
        break;
}