Should I suggest a time when professor want to schedule an interview, or just say I always available ? I applied to a lab and a professor want to set up an interview (for the first time). In the reply email, he said that: 


  "Please let me know when you are available. I am available on
  Monday-Friday, after XX:XX."


I would say when I am available: 


  "I would available everyday from XX to XX".


Should I also suggest a timeblock or not ?


  "I would suggest that we meet on Friday at XX:XX."
In this situation, pick a preferred time within the professor's constraints, and suggest it.  To be safe, propose a back-up (perhaps the following day) in case anything goes wrong.

Additional tip: Suppose the professor said he's available after 10 am.  Then to give him a little margin for error, I advise choosing a slightly later time, such as 10:30 am.