No. Originally, the developers at Nintendo had intended for the two to be related, but eventually decided against it. This can easily be seen by common physical traits between the two and between...
No! Not even close. She is said to be a relative of Mario.
Zelda is much better in my opinion but peach is good in many ways.
No, they are in two completely different games. Princess Zelda is in love with Link, a born adventurer, Princess Peach is in love with a plumber
That is an opinion but Daisy is better in speed whereas Peach is better in Skill