Because the 1.2 patch that was released today negates resistances of any kind, does this mean that you can be a vampire and a werewolf at the same time, as the 100% resist disease bonus for either condition is nullified? Also, does the lack of resistances also apply to weakness, i.e. Can I use the Apprentice Stone with no negative effects?

I expect not. In Oblivion, there was a Variable 'PCVampire' that got set to -1 if you cured Vampirism; even if you got the disease, the Script that controlled the change would detect the -1 and stop; I expect they have done the same this time, to stop you getting both.