1- Is there any way to see the execution time for reports that users run?
2- Is there a last run date-time stamp for reports?
3- Where do user profile settings get stored? For example, the picture, the profile description, etc. The host db or a flat file?
Unfortunately I don't have super good news for you on your first two questions. There are a couple of fields that would appear to present this information in the 'reportheader' and 'reportinstance' tables in Yellowfin's back end database, but they appear to give inconsistent/inconclusive results in my testing. That's not to say that the tables aren't doing their jobs properly, but rather the column names may be a little misleading.
In regards to your third question, user profile information is stored in a couple of different tables in the back end Yellowfin DB.
Does this answer your questions? Please let us know if there is anything else that we in Support can do for you.