well, 1st I would look in the admin console under system status | Advertisement status, then look for the name of the advert. You can also go into Status Message queries and get info,
As far as the reporting server look in the options under Software Distribution - Advertisement Status.
For telling you if the software was REALLY installed the machine would have to run a software inventory which would send a delta of the new software. You can wait for the regularly scheduled one or force it manually