Reading through this ATM thread, I feel I would like get a grounding in contemporary understanding of supernovae.

Here are three, separate, questions (actually, requests for sources). In each, I would like to know
a) what is the best, current textbook (OK, Top Five would be good too) on the subject area, as would be used to teach graduate students?

b) what are the most recent, relevant, review papers and/or conference proceedings (or other forms of overview/status, beyond textbooks)?

c) what are the truly open questions in the field, as exemplified by landmark papers?

The three fields:

Observationally, what are supernovae? How many different types are recognised, from their observational characteristics? What are those characteristics?

Theoretically, what are supernovae? How (well) do the (classes of) theories match the observational details?

Cosmologically, how reliable are Type 1a SN, as standard candles?

I readily appreciate that this field may not be as crisply separable as my questions.

Hum,
i can`t divulge the link to the latest supernova data...
But here is an old link i found with some nice clear images that outline the nature of supernovas, as well as their use as a indicator of distance and independent verification of redshift data.
http://www-supernova.lbl.gov/