The actual use has more of a connotation of somebody that isn’t contributing positively to society. For instance, just going off the acronym, you could call a stay-at-home parent or a retiree a NEET. However, the term NEET is usually used to refer to a young adult that is perceived to be wasting their time doing nonproductive things rather than contributing back to society or bettering themselves in some way.

No. A student might also be jobless.