Did Captain Janeway violate the Prime Directive by stealing the Borg transwarp coil in "Dark Frontier, part 1" since she and the Voyager crew have no right to steal from any species just for their own personal needs, without there being any kind of special circumstances?
The Prime Directive (although never quoted verbatim in complete length in canon, and apparently quite long) forbids Starfleet officers from interfering with the development of pre-warp species. The Borg have not just discovered interstellar spaceflight, they reached a level of technology which is even higher than that of the Federation, so the Prime Directive does not apply to them.
Also, the theft of that one transwarp coil was definitely not a notable interference with the development of the Borg species as a whole.
There likely are other directives which address under what circumstances Starfleet officers are allowed to steal from other species or commit other crimes on them, but that's not what the Prime Directive is about.
Memory Alpha describes the Prime Directive as follows:
A complicated order, the Prime Directive had 47 sub-orders by the latter part of the 24th century. (VOY: "Infinite Regress") However, a high-level summary was "no identification of self or mission; no interference with the social development of said planet; no references to space, other worlds, or advanced civilizations." (TOS: "Bread and Circuses") The directive provided guidance on what constituted prohibited "interference" with a society, covering such matters as:
- Providing knowledge of other inhabited worlds (even if individuals or governments in the society were already aware of such) (TOS: "Bread and Circuses"; TNG: "First Contact") Providing knowledge of technologies or science (TOS: "A Private Little War"; VOY: "Caretaker")
- Taking actions to generally affect a society's overall development (TNG: "Who Watches The Watchers")
- Taking actions which support one faction within a society over another (TOS: "The Omega Glory"; TNG: "Too Short a Season")
- Helping a society escape the negative consequences of its own actions (VOY: "Time and Again", "Thirty Days")
- Helping a society escape a natural disaster known to the society, even if inaction would result in a society's extinction. (TNG: "Pen Pals", "Homeward"; Star Trek Into Darkness)
- Subverting or avoiding the application of a society's laws (TOS: "Wolf in the Fold"; TNG: "Justice")
- Interfering in the internal affairs of a society (TNG: "Symbiosis", "Reunion", "Redemption", "Redemption II", "The Price"; DS9: "The Circle", "Inter Arma Enim Silent Leges"; VOY: "Thirty Days")
None of these were violated in Janeway's actions, meaning she definitely did not violate the Prime Directive.
Additionally, looking at the various Starfleet protocols and regulations that we know of, Janeway did not break any of those.