You can go into SSMS and check the Property of the DIM / FACT and get the time of last process.

The PROCESS FULL and other PROCESS functiona do the same type of processing, but FULL processes ALL (whether needed or not) and the other items handle other functions:

http://blogs.msdn.com/b/karang/archive/2011/01/25/kind-of-ssas-processing-in-simple-words.aspx?Redirected=true

Seems to be a good article on the differences