I learnt that in astrophysical spectroscopy, the emission spectrum of distant stars is used to determine what they're made of. So why is it that our own Sun is emitting the whole spectrum ? (or is that information incorrect)
There are continuous spectra, emission spectra, and absorption spectra. Dense materials, such as the deeper parts of our sun, have continuous spectra. Hot, low-density gases have emission spectra (a black spectrum with bright lines in it). The continuous spectrum generated deep in our sun passes through the cooler and lower-density outer regions of the sun, where it is partially absorbed. The result is an absorption spectrum: a rainbow with certain dark lines notched out of it: http://en.wikipedia.org/wiki/Absorption_spectrum
A good way to think about this is that a line spectrum comes from individual atoms, which are quantum-mechanical. In systems with a very large number of particles, the quantum-mechanical behavior becomes undetectable. A dense gas, such as the deeper parts of the sun, has all its atoms so close together that they act like one big object with a very large number of particles. Therefore you get no quantum-mechanical features, and it's just a continuous spectrum.