Yes, you will be able to cut a portion of the rhizomes whenever you want to. But you'll probably want to leave some in the ground to keep the plant going. I have one in a pot and I scrape away some of the soil to expose the rhizomes, then use a knife to cut off the portion that I need.

What other plants can be grown from dinner trimmings? Not sure what you mean by that. Do you mean from grocery store produce? If so, then seeds of any store-bought fruit such as citrus, pomagranite, star fruit, avocado, mango, durian (though not all will grow true to the original variety), root crops (ginger, galanga, taro, etc.), cuttings of sugar cane, etc. There is an Asian market near me that sells quite a variety of unusual produce. That's where I find the coolest stuff!