Is someone with the Inoffensive to Animals virtue also inoffensive to a Bjornaer when the latter is in his heartbeast form? I tend to say yes, as the Bjornaer is for all intents and purposes "Animal" in its Form. Plus it will be really cool for my magus. 
Most Bjornaer will have their Parma up all the time anyway so it won't make a difference... unless you're Blatantly Gifted (?)
I'd say yes -- and so that you be warned, I had planned a noble and faerie-blooded companion with alluring to animals... it might still be viable. 
AFAIK, Parma also blocks the effects of the Blatant Gift (as well as Alluring to X).
As far as I know gifted people are not affected by the gift themselves.
That's no longer true in 5th edition. Gifted people are affected like anybody else. That's the reason why, prior to Bonisagus' Parma Magica, there was little cooperation between wizards. Bonisagus' discovery is what made the Order possible.
The -3 penalty also applies to teaching, and it is a Low Crime not to share your Parma with your apprentice when teaching him.
Does parma magica totally nullify the effect of blatant gifted individuals giving you the creeps?
For we had a discussion whether parma would nullify it or make it about as bad as a 'normal gifted.'
It would explain why most of the magi in our covenant think the the blatant gifted magus cannot communicate with mundanes because she constantly refuses it, thinking they will run away. (with an attitude like that they will indeed run away, take a possitive view on life and others 
)
I'd go for nullify. But that doesnt neccesarily mean that other magi have no concept of the Blatant Gift or maybe even who might have it.