7 wonders

After looking at the painting (the 2nd wonder) and seeing it change, go down the stairs. You'll then see (sometimes) the man from behind the counter walking up the stairs. Follow him, making sure that he doesn't see you.

The 3rd wonder is just getting the Gold Shard item by defeating 3 strange Bombs on the path to the mako reactor (talk to the kids to find out more).
The 4th wonder is opening the safe inside Shinra Manor. The 4 combinations are linked to a card with riddles inscribed on it. Look through 4 keyholes and count how many unshelved books/monsters/banora apples & cans/chairs are in each of the locked rooms. You may need to guess for the unshelved books.
The 5th wonder is underneath Shinra Manor. Follow the storyline, and kill the enemies you encounter. They will drop Coffin Keys (4 in total). Enter the crypts and find someone familiar sleeping inside a coffin.
The 6th wonder is only available if you complete the first 5 wonders. Once Nibelheim is on fire, talk to the boy and opt to save his mother. Since you can't see inside the burning building, just move the joystick around so that you go upstairs and into the attic.
After a while, you'll get an email from the boy, telling you he left materia behind for you. Check the buildings on the outskirts of Nibelheim. Behind a fence, there's something glowing.

The combination is 5762 to the laughing safe wonder.