Did the Duke Do That to Georgina in Real Life?

In real life there is no evidence of a rape of any sort. Georgina wanted a male heir just as much as the Duke did. He would not have had to rape her, nor was he the rapist type based on what i've read.

Back then, a woman had no right to refuse her husband his "rights". So technically, there was no rape. But it is not completely out of the question to think that he forced himself on here. It was often done back then to put a woman in her place.
Sadly, women in history have been seen as little more than chattel. They were to be an advantage to their husbands...and were to accept anything that their husbands decided...(hence, her having to deal with living with Bess, which by the way would have been a huge scandal.) and had little to no say in matters other than decorating or fashion.

*The only cure for ignorance is knowledge.*

Unknown. But as others have stated, it was not legally considered rape.

However it was obvious by the terrified expressions on the servants, the children and Bess that they knew Georgiana was being attacked.