I agree with Michael. Also, since English isn't as clear-cut about formality levels as Korean, what may sound more formal to one person could seem not as formal to another (although to me, the order of rising formality you stated sounds about right). However, none of the sentences would sound rude or too informal if you were speaking to a respected person.

Essentially the same, no English speakers would think that any of the sentences were odd or would misunderstand your meaning. I would probably say either of "He is prone to bouts of cold" or "He is prone to getting bouts of cold"