Henry could not get an annulment, as far as the church was his marriage to K of A was legitimate.
Another thing Elizabeth was concerned with is that her mother was 2-3 months pregnant when she married, so she wouldn't want to draw attention to that as it may question her legitimacy. She must have been grateful for that red hair.
England didn't become a protestant country overnight, it mostly happened during Edward's reign.
I think Jane Grey was a pawn to start with but she soon started signing her name as 'queen Jane'.
The men who had been basically ruling England while Edward was on the throne wanted a legitimate protestant on the throne, that was Jane.
If Henry was legally married to K of A then the legitimate heir was Mary, but if it wasn't then it was Elizabeth.
Both were named in Henry's will, but I doubt he thought his son would die 'without issue', I think it was to give them status at court and because he seems to have genuinely loved Jane Seymour and she wanted better relations between Henry and his children.
I find David Starkey's programmes crap, the title is the wives but he only talks about them in relation to Henry, hardly a mention of childhood, education or anything before marriage.