The weight depends on components, larger graphics cards weigh more for example. But it should be around 40 lbs. 

You will not be able to add any foam to it, as it is already packed with special molded foam that holds the contents securely in place during shipping.

There should actually be 2 boxes. 1 rather fancy Alienware box, and another plain brown box. It will be double boxed.

It's shipped pretty secure already. I don't think you can improve much on it besides maybe putting it inside a wooden crate?

Thank you! I think you are right! The wooden crate would be just too much...

What about the graphics card? Do you think I should remove it? Or does it hold it very well so I shouldn't worry about it? (It's an RTX 3080)

Awesome, thank you! What about the dimensions? Any idea?

They all ship with the graphics card installed, without any issues. They use a pretty beefy support bracket to hold the video card in place.

Mine came with an RTX 3080 without any issues. With the padding and the double box it can take a beating without occurring shipping damage. The neutral outside box also hides there's an expensive gaming system inside the box.

The GPU is fine in the PC, it ships that way, and is secure in the PC, which is in the padded box with form fitting padding.  If you did remove the GPU, you should remember to wrap it in an anti-static bag to protect it, in addition to padding. 

I don't have the exact shipping box dimensions, I'd like to say it was around 2' x 2' by 18", but it's been a while since I've seen one in the box so that is just a hazy guesstimate.  If helpful to extrapolate, here are the dimensions of the PC: 

https://www.dell.com/support/manuals/en-us/alienware-aurora-r12-desktop/alienware-aurora-r12-setup-and-specifications/dimensions-and-weight?guid=guid-a2ec334b-aeb0-402e-a579-9d896d8c2df0&lang=en-us

Shipping box that mine came in: 16.5” x 22.5”x 24”