Need Help with Illustrator

Not exactly sure what you mean but you can copy the web page as an image using 'print screen' but that's limited to what shows up on your screen at once. You could do several and stitch them together.

From this image you could create multiple layers and mark them invisible until needed.

On the other hand, you could save the web page in its entirety to your computer and modify the code as necessary.

I don't have adobe illustrator but I do have adobe elements and adobe photoshop and I know it can be done in those.