Prince Harry threatens to post his statement about the paparazzi on Twitter if Kensington Palace will not release it. In actuality, none of the royal family are allowed to have social media accounts and Prince Harry has no Twitter account.
Harry tells Meghan that they need the queen's permission to marry due to the Royal Marriages Act 1772 and Harry being fifth in line to the throne. That law had no such stipulation based on place in the line of succession -- it required all descendants of King George II to obtain the monarch's permission to marry. That law had also been repealed and replaced with the Succession to the Crown Act 2013, which does contain the stipulation Harry is referring to.