Go to where you bought it and buy another cape and you'll get another hood.
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The items kept on death are based on the high alchemy value of items. In game, if you click on the equipment tab, and then the 'items kept on death' tab, it will show exactly which items will be kept upon death. Most generally there your 3 highest (high alchemy) valued items. Things like a PKers skull changes that number to 0. Remember, if you die you can always retreive your items is you make it back to your place of death before your grave crumbles. If you do lose your skillcape, you can always buy it back from the master for 99k.
You can't.
guthix d'hide,with green h'ween mask
A skillcape can be worn to show off 99 in any skill.
Some of them you get from quests, some from holiday events. And one you can only do if you are wearing a skillcape.