Those particular headlines, whose stories I have not read, are easy to dismiss as inherently biased.
Parodies are not unique to Harry: they are an inevitable side effect of successful books. The book is the Guinesss world record holder of the best selling work of non-fiction ever published. Of course it is going to invite parodies. And it's easy to parody because of the nature of the material.
Jane Austen, Harry Potter, Shakespeare, Tolkien, even EL James who may as well be a parody herself have been parodied. No one has ever parodied an unsuccessful book. Not once.
On the visa thing: it's a right wing think tank that made an application to see Harry's visa application. The relevant authorities correctly responded by asking them to submit a form signed by Harry consenting to the release of the information because without that they do not release private information.
Harry will not be deported, his visa is not in trouble, if only because in America, money talks, he is not a hapless immigrant who will get shafted. He is a prince of the United Kingdom with lots of money and good lawyers and there are no circumstances under which he will be deported leaving behind his American children and wife.
More on parodies here! (Oh, I love this new MN feature)
https://www.tckpublishing.com/parody-books/