the box holds things together and allows you to exclude oxygen, so that the welds take without the need of a flux like borax. Borax sometimes leaves a white line/haze around weld lines and if you are using powdered metals then it would make a heck of a mess. A small piece of cardboard or squirt of oil is often sealed in the box to take up and extra oxygen whilst the billiet is coming to welding heat, that way you don't get the surfaces oxidising and refusing to stick. The box gets ground off once the welding is done, same as any mig welded seams and joints. If you don't grind them off as soon as the welding is done, then they can mess up the pattern development or even get forged into the final piece (making a soft bit that looks awful!).
The quality of the steel will depend on the stuff you put in, mostly it will be a high nickle steel for the bright layers (say 15n20) and a similar plain carbon version (say 1095, cs70, etc) for the dark layers; then you can have pure nickle sheet for silver/white layers and other steels for more of a grey for some patterns. the silver stuff you mention is likely some pure nickle. You can do stainless damascus, but it is more difficult to weld and then forge because it move strangely at heat and oxidises badly, so refusing to weld unless you keep all of the O2 out (some people even use argon barriers!)
Nickle won't harden, but the rest will (they are all good blade steels afterall). In the instances where you have components that don't make a good edge steel, you simply add a seperate cutting edge to the blade after the damascus patterns have all been done. That is why you will often see a plain (or normal damaascus pattern) at the edge with the rest of the blade being poncy mosaics and thigs
Or you laminate it as a san mai, with blade steel in the centre. So the edge will be whatever hardness you can from that steel. If its a simple CS70 or c20 and 15n20 billet (such as most non-mosaic is in this country and around europe), then it will all get to at least 60rc and often higher depending on your set up