This is all dependent upon how the phage initially attaches to the cell. I image that if the cell is dead, the phage receptors on the cell membrane would change and therefore the phage would no longer be able to bind. In the case of Caulobacter phiCbKviruses, they only bind and infect younger bacterial cells. Personally, I don't think that a phage would bind a cell in which it can not replicate within.
Yes they can. Bacteriophages can very much bind to dead cells, often irreversibly. Most of the time the phages are binding to a surface molecule which does not require a cell to be alive. Debris from disrupted cells can often inactivate a phage lysate by providing binding receptors for phages to attach to as part of the cell debris. There are exceptions of course and so it somewhat depends upon which phage and which receptor is being used.
It is an entirely different matter as to whether or not the phage can inject the DNA, that depends upon the energetics of the reaction and therefore on the type of phage.