Importing From Illustrator - Keep layer order

The standard AI to AE workflow is as follows:

1. Create your AI artwork with each element you want to animate on a separate layer.
2. Generally, you do not want to convert Vector Layers to Shape layers unless you want to animate the actual paths, use shape layer animators, or extrude an object using the 3D rendering options available in the C4D renderer.
3. If you are going to convert any AI layers to Shape layers you must not use Brushes, gradients, Layer Styles, Clipping Paths or any other fancy stuff unless you are willing to rebuild all of the gradients or other fancy stuff in After Effects.
4. Any Artwork created in AI that extends beyond the Artboard boundaries will be cropped. You want to check your artwork with Pixel Preview turned on and create it with Snap To Pixel enabled in the View Menu
5. When you import an AI file, you should almost always choose Retain Layer Size and make sure import as a sequence is turned off. 
6. Importing an AI or Photoshop file as a composition creates a new composition in the Project Panel, but it does not open the comp. You must double-click the created composition to open it and complete the animation.

From your posts, I can see that you did not originally open the comp AE created, and you imported the AI file as an image sequence. Follow the workflow above, and as long as you properly prepared the AI file you should get a composition that can be edited.

A sequence is a sequence of individual files. That won't solve your issue. Otherwise it's pretty clear: Your layers are not in the correct numerical sequence. You need to pad the numbers with leading zeroes. Not AE's fault, just how AI names the layers. You may want to find a renaming script for illustrator that takes care of such tasks.

Mylenium

Without any info about your actual layer structure by ways of screenshots in AE and AI as well as details on what specific features are used in the illustration we can't tell you much. The only time the layers would be reordered is if it would be required to retain the appearance, but that is pretty rare. Otherwise AE already imports the layers in the order they are arranged in AI.

Mylenium