Can i use init hook for API purpose?

If you want a more user-friendly URL structure, you could add a rewrite endpoint.

This will add the rules for and intercept requests to /my-api/:

function wpd_add_api_endpoint() {
    add_rewrite_endpoint( 'my-api', EP_ROOT );
}
add_action( 'init', 'wpd_add_api_endpoint' );

function wpd_api_request( $request ){
    if( isset( $request->query_vars['my-api'] ) ){

        // $request->query_vars['my-api'] is a string containing everything after your url slug
        // convert it to array
        $parts = explode( "https://wordpress.stackexchange.com/", $request->query_vars['my-api'] );

        echo '<pre>';
        print_r( $parts );
        echo '</pre>';

        die;
    }
}
add_action( 'parse_request', 'wpd_api_request' );

After you flush rules, try a request like:

http://example.com/my-api/something/else/123/4,5,6/&7

Which will output:

Array
(
    [0] => something
    [1] => else
    [2] => 123
    [3] => 4,5,6
    [4] => &7
)