MR -> PPR usually takes a month, month and half (approx) as per the latest trend with NDVO. NDVO is quick now as majority of the application have already been processed. Though it depends totally on your IMMIGRATION OFFICER's LOAD. Its same like a customer care agent assigned tickets, in our case assigned files which they must process till the end.
Background verification is MANDATORY for each and every applicant. It usually happens once you submit your PCC and is been carried out by third party. Though it is not clear when do they conduct it before of after MR, but its initiated only after your submit your PCC.