About detemining the time of interview I have been asked for a faculty position interview. Regarding the time, in their email they have only asked me about my availability for two days without a specific time. I want to know that in my confirmation reply, should I provide a specific time for interview or I just determine the day?
If it's a job you want, either clear your calendar for the two days they are proposing, or propose two days when you are free all day.  It's not clear from your question if they are proposing the days or asking you to propose them.