Yes, the Tudor rose conjoins the white rose of York and the red rose of Lancester and symbolizes the end of the Wars of the Roses and the union of the houses. I've found an interesting quote about the white rose/red rose idea as a Tudor invention on Wikipedia - and here we come quite close to Beth's question of Tudor iconography! http://en.wikipedia.org/wiki/Tudor_rose
Thomas Howard, 3rd Duke of Norfolk wears the Tudor roses not because he's related by marriage, but because he's Lord High Treasurer and thus the most important official of the government. The collar comes with the office. Here are two of his successors:
William Paulet, 1st Marquess of Winchester
William Cecil, 1st Baron Burghley
Your first picture was formerly known as portrait of Catherine Howard, which is now disputed - general consensus seems to be that it depicts an unknown lady, probably of the Cromwell family.
The second to last portrait of Henry VIII in your post is the left section of Holbein's cartoon for the wall painting in Whitehall - you've posted Remigius van Leemput's later copy of the complete painting in your first post.
It would be interesting to do some further research and dig deeper, but it seems that the Tudor roses as part of the jewellery might not necessarily have been added to the paintings as an iconographic reference to the Tudor claim to power (at least Anne Boleyn was portrayed without them) and could have in fact existed in the way they were depicted (unlike the roses in Henry VII's and Elizabeth of York's hands). The fact that noble ladies in later years wore similar elements could be a hint that their use at court made them fashionable and maybe perceived as an epitome of power and wealth.