How to Import and edit transparent PNG

[Kobrabiss5CC0]

Hey guys,
I have a hard time getting imported files to an editable state. I want to add an transparent Icon to Illustrator and put a dropshadow on a cretain part of it, but I can't select it.
I'm as far as tracing and expanding the image, which would make parts of it selectible and editable, but that always destroys either all transparency (adds white background) or all white parts of the image (by ignoring all white), which is a problem because the white is what I want to put a shadow on and it edges on with the transparency.
I can do all these things in Photoshop without a problem, but I guess there is a way to properly import transparent images to Illustrator without destroying them.
Thanks in advance!

[Monika Gause]

You have to vectorize it.

Can you please show something? There might or might not be a simple way to do it.

[Kobrabiss5CC0]

This for example. If the diamond shape on the top had an outline I'd be able to select the "white background" that get's generated when vectorizing and just delete it, but as it is now, the transparent background and everything white touching it mold into one shape.

[Monika Gause · Accepted solution]

These are just geometric shapes.

You can build that quickly and will get better quality than when tracing it. Then you can do what you need with it.