When kids are stuck, or encounter a problem, they often start to give up. You can talk to them, and try to have them explain to you what the problem is, talk them through solving it. If this doesn't work, taking a break and coming back can help, and maybe having them join another person as well might benefit them.
2.) Learning is finished when the student is in the darkest circle of the Proximal development zone, and fully understands the subject to the best of their ability. The product does not matter as much as the journey does. If the Journey teaches them the topic the same, or better yet teaches them better, then you should be able to be flexible and change the lesson to better accomodate this.