The crown princess is the princess who will become the queen as she is the eldest child of the current king and queen. Let's say that king Carl's first daughter is named Victoria. She is the crown princess as she will one day become queen. Carl might have a son named Phillip or even another daughter named Madeleine, but they would (only) be a prince and a princess as they will not inherit the throne.
In Sweden it is the first born child, regardless of gender. This has recently been changed in the UK (and commonwealth), but note that before, like with the real Queen of the UK, she is only queen because she had no brothers. It is called Male Primogeniture if it is the first son, but in the case of Sweden (and the UK as of 2015) it is Absolute Primogeniture. Sweden was the first modern nation to adopt Absolute primogeniture.
No, actually the Netherlands were. We have Absolute Primogeniture since 1890 (the year that king William III died) though Sweden has it since 1980, actually Carl Philipp should've been Crown Prince, which he was for three years, and after the abolishment of the Male Primogeniture, his older sister Victoria became Crown Princess
"In 1980, Sweden amended its constitution to adopt royal succession by absolute primogeniture, displacing King Carl XVI Gustaf's infant son, Prince Carl Philip, in favor of his elder daughter, Princess Victoria, in the process. Several monarchies have since followed suit: the Netherlands in 1983, Norway in 1990, Belgium in 1991, Denmark in 2009, Luxembourg in 2011, and the United Kingdom and the other Commonwealth realms in 2015."
The children of the King are all HRHs. Prince Carl Philip's wife was also made an HRH on her marriage and entry into the Royal Family. Unlike the others spouses, Princess Madeleine's husband did not join the royal family upon his wedding (he was and still wants to be active in business/finance) and so wasn't made an HRH. I'm not sure he's ever even lived in Sweden.