A cross country skiing boot. Along with the ski's amd poles that match.
It all depends on how tall you are and what type of ski you want to ski on. Im about 5'5 and my GS skies are 165's
Bindings
A ski boot size 330 is about a US size 10.5-11.
It is not a shoe. It is a ski boot.
The HEAD AdaptEdge Ski Boot is quite unique. It allows you to change the width of your boot from 104mm to 102mm with one turn of a screw.
The "last" is the width of the forefoot of the ski boot. Generally a 98mm is narrow, 102mm is medium and anything over is wide or high volume
Usually, to remove the boot from the ski, there is a lever behind the heel. When putting on the ski, it is pushed down, but it clicks upwards when the ski is attached. Thus, to remove it, push down firmly on the lever until it is in the downward position while slightly lifting your foot.
Take your boots to a ski/boot shop that sells the same brand. They can replace the heel piece, or at least order a replacement for you.
Yes...
Yes, they can, but if they are going to be adjusted you should (pretty much have to) take them to a "certified binding mechanic." The people at your local ski shop will be able to adjust them.
Cross countries skis require a different type of boot. These boots only attach to the ski at the toe allowing your heel to move off the ski as you move. On downhill skis your entire boot is attached to the ski. You can read more about the differences here http://skiing.about.com/od/beginning skiers/a/ccdownhill.htm
Downhill bindings are adjustable for different size boots. Cross-country bindings only lock into the toe of the boot, so one binding works with any compatible boot.