Explore chapter one and then you should be able to move onto chapter two.
No you can't. If it isn't an important chapter you can skip it, but if it is a compulsory chapter you have to do it before you move on.
You don't really do anything in chapter five. You just go on to the next chapter.
Curses and Countercurses is in Chapter 12, Moment 2 (Christmas at Hogwarts), lying on the bench.
The Pottermore Wiki contains guides which goes though each chapter and also contains lists on every collectable item.
Vernon & Petunia Dursley can be unlocked by clicking on the family picture on the small table.
You have to finish all the stages in chapter 15 in order to move onto the next chapter.
Yes, you can find many things. For a guide per chapter see the Pottermore Wiki.
Chapter 5 of Harry Potter and the Chamber of Secrets was released on the 18th September 2012.
You don't interact with the diary in this chapter.
Chapter 16 of Harry Potter and the Prisoner of Azkabanwas released on the 31st July 2013.
If you mean book two, apparently early 2012
In chapter 8 on the top stair