As far as I know you can not use it to start another batch. I know that Bodyology's kefir starter you can use the kefir to start a new batch, but I don't believe you can with yogourmet.
Kefir should develope curds when it's finished. I have only used live kefir grains and I would get a definate seperation. Then I would mix it up and it would be thinner than yoghurt. However, I too bought yogourmet kefir started and started a batch on Friday. I let it go until this morning and still didn't get seperation. I used goat milk and it's not too thick, but goat milk produces a softer yoghurt so I'm not surprised. This batch of kefir smelled more sour than yeasty which is what my live kefir grains smelled like (which may explain the problems I had with candida and live kefir grains).
However, because it was warm in your home it may have speeded up the process. You might want to experiment and let it go longer to see what would happen. You won't ruin it by leaving it out. If you've left it out too long you will get kefir cheese and whey.
You won't be able to grow your own grains from the kefir starter. The starter is essentially the bacteria and yeast found in the live grains, plus some freeze dried grains. The freeze dried grains are not alive so they won't reproduce new kefir grains.