The short answer is, yes. You are correct on the focal length issue. Any FX lens will 'act' like it is 1.5x larger when used on a DX camera.

There is no aperture penalty for this; f/2.8 (coupled with the same shutter speed and ISO) will produce the same exposure on the FX and DX cameras. Yes, you can use the widest aperture on both cameras equally.

The reason for this apparent increase in focal length is that the FX sensor is 1.5x bigger than the DX sensor. The FX lens is designed to produce an image that will cover the FX sensor, and when you use this lens with a DX sensor, you use only the center portion of the image.

You would get exactly the same effect by using an FX camera and cropping the center area out of it. The image would 'appear' to be 1.5x closer because of the cropping.

To continue the camparison of the DX and FX image when using an FX lens on both, you have to also consider resolution. If a DX camera and FX camera have the same number of pixels, and you crop out the center portion of the DX image to make the same field of coverage, then the DX image will have more resolution. Some people discuss this by how many pixels you are putting on the subject.

Lastly, there is the issue of depth of field. You will see a greater depth of field than when an FX is used on a DX sensor than when the same lens is used on an FX camera. However, if you crop the image from the FX camera to make the same field of coverage as the DX camera, the depth of field will be the same.