How to add custom fields to the all users page

For the first part of your question, you can add new columns to the users table.

Its in two steps: first you need to register the columns, then output information for each row.

To add new columns, you hook into the manage_users_columns filter:

function yourdomain_manage_users_columns( $columns ) {

    // $columns is a key/value array of column slugs and names
    $columns[ 'custom_field' ] = 'Custom Field';

    return $columns;
}

add_filter( 'manage_users_columns', 'yourdomain_manage_users_columns', 10, 1 );

Then you need to output your custom field using the manage_users_custom_column filter:

function yourdomain_manage_users_custom_column( $output, $column_key, $user_id ) {

    switch ( $column_key ) {

        // look for the slug you registered
        case 'custom_field' :

            // get your custom field, parse it however you want
            $value = get_user_meta( $user_id, 'custom_field', true );

            // return the value
            return $value;

            break;
        default: break;
    }

    // if no column slug found, return default output value
    return $output;
}

add_filter( 'manage_users_custom_column', 'yourdomain_manage_users_custom_column', 10, 3 );

As for user activation:

Maybe the WP_options table isn’t the best way to go about it, as it will grow quickly, slow your website be hard to maintain.

You might want to create a new User Role for non-activated users and set it as default; which you can change easily through the admin interface.

If you are adding this code via a plugin, you might do:

function yourdomain_add_user_role() {

    // capabilities
    $caps = array(                   
        'level_0'   => true,      // inherit subscriber capabilities
        'read'      => false      // but can't read posts, etc
    );

    // ads the inactive user role
    add_role( 
        'inactive',               // Role slug
        'Inactive Account',       // Role name
        $caps                     // capabilities
    );
}

register_activation_hook( __FILE__, 'yourdomain_add_user_role' );

Have a look at the codex for a (long) list of user roles and capabilities: https://codex.wordpress.org/Roles_and_Capabilities

Hope that helps!