I don't think Henry F. would have been placed before Edward or even Mary because the majority of the people would not have liked a child conceived and born out of wedlock as their ruler. The people, even though Henry VIII said otherwise, recognized the legitimate status that Mary and Elizabeth had. Henry F.'s mother had not even been a Queen (at some time or another).
As for Mary Tudor, no it was not her father's wish that she come to power. He wanted his son to be king and for the succession to go to HIS sons. He only restored Mary and Elizabeth to the throne because he realised that he had to. If he didn't, the throne would have been passed onto the Catholic side of the family, something that he did not want to do.
And I don't think that Mary was beloved by the people - remember the Smithfield Fires? One of the reasons that Elizabeth never named a successor was because she knew what it was like being a successor. The majority of the population liked Elizabeth MUCH better than her sister Mary and they just waited as best they could until Mary died and Elizabeth became Queen. There were plots and the like to get Mary off the throne and pass it on to Elizabeth - that's why she was under arrest at one point, Mary thought that Elizabeth was plotting against her.