Remove  around form items
Yes. These classes are hardcoded into Drupal and are not only used for visible styling but also for the jQuery code that "animates" the forms (validation, autofill, auto focus, etc.)

HTML elements can have multiple classes. You could just add the classes to the Drupal form and then create your own theme. By creating your own theme you could not theme the default Drupal classes and instead just theme the classes from Base CSS.