There are a few tasks here, but the last one probably is that you'll have to win at a game of Wizard's Chess. If you play chess, this will be very easy. The next game in the library will be harder, and in the Great Hall, the hardest.
Ginny is in the Gryffindor common room.
the fat lady
The director of the first two movies didn't return and so some of the sets, including the Gryffindor common room, were changed to fit the vision of the new director.
Kreacher is upstairs in the Black's tapestry room.
There is no room of rememberance. I think you are speaking of the Room of Requirement. The room in question is in every book, but is only discovered by the students in the 5th book (Order of the Phoenix)
The Gryffindor common room.
Ravenclaw's common room is in a tower like Gryffindor's is.. In the ootp game there is only Gryffindor's room
Ginny is in the Gryffindor common room.
you get missions and the invisibility cloak
No, you cannot see any other common rooms in this game other than the Gryffindor room.
The Gryffindor champion is in the Gryffindor common room by the notice board. The Ravenclaw champion is in the library at the table. The Slytherin champion is is the Great Hall near the table where Dumbledore's chair is.
One of the champions is in the Gryffindor common room, one in the library and one in the great hall. You have to beat the one in the common room first and then the Slytherin one in the great hall to get to the Ravenclaw one in the library.
There are three. The easiest one is in the Gryffindor common room. Another one is at the Slytherin table in the Great Hall. The hardest one is in the library.
The game finishes but you can stay there and the next time you'll load the game, you'll start from Gryffindor Common Room. You can take duels after that, complete your discovery points etc.
the fat lady
In the Harry Potter novels, the sleeping area for girls is located off the common room of the Gryffindor dormitory at Hogwarts. The Gryffindor common room is located in a high tower on the 7th floor of the east wing.
It isn't accessible in Order of the Phoenix.