Q: Why entire library is in one project folder?

Which version of iPhoto and Aperture are you using?

What do you mean by "Project folder"? Are you looking at folders in Aperture and iPhoto? Or at projects in Aperture and events in iPhoto?

iPhoto will show any Aperture project as an event, and both should be showing the same number of images, unless you have hidden photos in iPhoto or rejected images in Aperture.

If you select a folder with projects inside, Aperture will display all images inside the albums and projects in that folder at once. 

So, to answer your question, we need to know exactly what you are looking at, both in Aperture or iPhoto.

Sorry, your screenshots are not showing for me, due to the buggy  software for these forums. I hope someone who can see your screenshots, can answer this.

It's not. You are looking at the projects "thumbnail view." Each "picture" in there is a representative thumbnail for a project. If you put the mouse on top of one of them and move it left or right, you'll see Aperture scrolling through the photos in the project.

Go select one of the projects at bottom left to select that specific project.

Nothing is messy here; Aperture is showing you the entire library, by project, in the "Projects" view.

I can't see the screen-shots either.

Here is the User Manual chapter on the UI.  The page on Projects View is about half way down the list.

Added:

How are you opening the Project that has 29 Images in it?

Added:

Your screenshots show if I give the page several minutes to load.  (Strange behavior.  I have a fiber-optic Internet connection.)

I suggest repairing your database.  Apple's instructions are here.

I have never harmed a working database by running Repair.  Nevertheless, standard computer practices should be followed.  Never use any computer file without have a backup.