This month, i saw the pagerank of a number of my sites being improved, and it means that google has updated its pagerank for this month. Is anyone else has noticed it or is it just me or is updating pagerank is not a whole affair from google and they update it on an individual sites basis?
PR is NOT assigned to individual sites it is assigned to individual pages.
You're quite right on both points. The 'published' PR doesn't actually affect your SERPS, it's just a snapshot. There's some good tools on www.iwebtool.com for checking published PR