1. What Citation style do I use?
That is a departmental decision. Some departments may even use more than one style.
2. Who is in charge of teaching students proper APA, MLA, Chicago/Turabian, NLM, etc. styles.
You are. While the library supports the faculty in this task, these styles are created by your professional organizations and so you are the experts within your own area.
3. How will the library support me in this task?
The library maintains Research Guides for APA, MLA, Chicago / Turabian, and National Library of Medicine.
Additionally the library will acquire up to three physical copies of your most current style guide for check out to students and post links to supportive online resources where available.
4. Is there any software available to help?
Brian Croxall, "Zotero vs. EndNote," The Chronicle of Higher Education, ProfHacker, (May 2011), http://chronicle.com/blogs/profhacker/zotero-vs-endnote/33157 (accessed July 13, 2012);
CAUTION: Almost all computer generated citations are incorrect. While creating a citation by computer can save you time, it is prudent to review and correct the result.