Thank you very much for each reply. it helps a lot.
The app's is there to show analytics from several (3 actually for now) aspects. one of the features is the most frequent word used. is that still legit regarding using the profile image?
When you state "...using user profile images commercially", the app will eventually be commercial (I hope someday if it will bring traffic).
I won't use the images as a main or a fixed header. only when you search for let's say kim kardashian, you will the first 3 users that come up, with their profile image which are display in the regular twitter search.
You then select the "right" user and then see his analytics (not private users of course).
Thanks in advance