Going back to princess issue, again it seems to be a male thing. The Offical UK Monarchy site has the following (carefully tucked away):
In 1917, King George V laid down the rules which govern the use of the terms 'His/Her Royal Highness' and 'Prince/Princess'. Only the children of the Sovereign, the children of the sons of the Sovereign and the eldest son of the eldest son of The Prince of Wales would receive the title. Thus all The Queen's children are 'HRH', 'Prince' or 'Princess', and the offspring of The Prince of Wales and The Duke of York carry the title. The children of The Princess Royal however, do not. Likewise, The Duke of Gloucester, The Duke of Kent, Princess Alexandra and Prince Michael of Kent are also entitled to use the title as grandchildren of King George V through the male line, but none of their children are.
Wives marrying a holder of this title would be known as Her Royal Highness but men marrying a holder of the title would not. The only exception to that is Prince Philip, who in 1947 was created HRH The Duke of Edinburgh. Letters patent declared that their offspring would be known as HRH. Otherwise as grandchildren of the Sovereign through the female line, the offspring of Princess Elizabeth and The Duke of Edinburgh would not have been entitled to use HRH or Prince or Princess until their mother became Queen, at which point, as children of the Sovereign, they would have been eligible.
So Edward is really breaking with tradition, though why the babe defaults to Lady where as Peter and Zara don't seems to defeat logic - they really do seem to make up the rules as they go! I'd read somewhere that strictly Louise, being entitled to use the form Princess, could ask for her parents' decision to be overturned when she comes of age, but goodness knows who will be on the throne (if we still have it!) by then.