I found it to be a more relaxed interview process than residency although I'm not sure if the competitiveness is on the rise again. In general, since most program directors only take 1 - 2 fellows and work very closely with the fellow, I think they're looking for someone they would enjoy spending a year with rather than trying to squeeze in the absolute best candidate.
For smaller private practice style fellowships, I would use common sense. It's very common to be asked where you want to settle down afterwards. Obviously no one likes training their own competition. I wouldn't advocate lying but I would be intentionally vague if you want to set up shop close to where you train.
I don't know if malpractice issues prohibit this practice now but I was asked to assist with surgeries during some interview days. I don't think they expect you to be able to perform a forehead flap from start to finish on your own but you'll want to make sure you brush up on anatomy and basic surgical competencies.
Finally, it depends on how badly you want the fellowship, but I was turned off by programs that asked stupid questions like "What is your biggest weakness" or seemed to enjoy being malignant to the fellow. As a dermatology residency graduate, I think you carry a very viable backup option of starting a lucrative career as a dermatologist. I would not put up with abuse for the "privilege" of being a surgical fellow. (For full disclosure, I LOVED my surgical fellowship and would encourage everyone to do a fellowship if it fit with their personal and professional goals. But I would have been very happy as a general dermatologist as well and would not put up with the nonsense that some of my peers struggled through during their fellowships)