The item menu just below where you select a mission (the one where Temp-er doesn't know what it does) allows you to make items with some of the raw materials that you gather. As you finish missions, you will unlock new stuff to make. For example, the first thing you can make is a riceball, and you need one of those bamboo sticks and some grass to make it. Also, shurikens require a single piece of rock, etc. When you are making stuff, you can sometimes make stuff really good and get stars on them. One star gives you a +1 to the item, making it more effective. I got 2 stars on a riceball, but I think you can probably go up to 3 stars.
I still don't know what the menu under the kill animation menu is for, but it looks like it would be for special items or stuff that you've collected/unlocked, etc.
The bottom right menu, with the ninjas in the back and stuff is to save your game (I think). It then gives you a menu with Iie (no) and hai (yes). If you pick no, you go back to the game, and if you pick yes, you quit to the main menu. So it just saves your game and asks you if you want to quit.