The Steam Deck has a "45W USB-C-PD3.0-Netzteil". USB-C is default and the Icy Box can handle up to 100W.

So, I don't see any reason why it shouldn't work.

I don't know, if you can use all other ports with the Deck, but that should be possible, since Steam Deck describes:
"USB-C mit DisplayPort 1.4 mit Unterstützung von Alt-Modus; bis zu 8K mit 60 Hz oder 4K mit 120 Hz, USB 3.2 Gen. 2"

So the Video Outputs should work too.

Sorry, I don´t know!