I have a question about Azura's Star: when it gets filled with a soul -- any soul -- is it instantly filled up and useless until the soul is used? Or can it infinitely absorb souls without end?
No it operates as a grand soul gem or a black one based on your choice after collecting it. Check the UESP here http://www.uesp.net/wiki/Skyrim:Azura%27s_Star#Azura.27s_Star