Depends on the company but I have had days when the answer to all 3 questions was NO! (Although that is not the answer they gave us of course).
Its our ultimate responsiblity to ensure flight plans are filed, that we have sufficient rest to operate next flight and that we don't operate outside of the legal rules. Sometimes ops/crewing try to push it that little bit further....
Now I am not saying that you do, but if you are regularly being asked these questions by pilots then either you are not doing your job properly, they don't know what you do, or there is a complete lack of communication between you.
Just a thought.