1. The applicator absolutely matters. Do not apply wax with anything you wouldn't use on your paint with any other product. In other words, yes, you can induce swirls while waxing if you have a cheap, terry towel or a bath towel or anything like that. Use a microfiber cloth or pad. Either one.
2. Yeah, you can put the synthetic wax on top of your natural carnuba. In fact, some prefer that combination. Gives you the depth you get from carnuba along with the gloss from the synthetic. In a dark color, like Jet Black or Chili Red

it is especially a good effect.