Your strategy: First, help your child manage his stress. Think of stress as being on a continuum ranging form 0 (relaxed and confident) to 10 (freaking out). When you're at level 7 or higher, it's hard to think rationally or be productive. This is where the "I can't do it" thinking starts to take over. So, help your child calm down so he can focus. You might try deep breathing, jumping on a bed, watching a brief funny video, or listening to a favorite song.
Once your child feels as though his stress level is below 7, help him problem-solve by breaking down the project into the specific steps that need to happen in order to finish. This will make the large task feel more manageable and achievable. To get the process started, ask your child questions such as What are the specific steps that will take you from where you are now to where you want to go? Have him write each step down, no matter how small, then tackle them one-by-one. As he finishes each step, he can check it off. This will reinforce his progress, and help him stay motivated to finish the project.
Your strategy: Kids can take feedback very personally, even when it's constructive. So when someone says, Do X differently, what they can often hear is (1) A negative comment, or "You messed up," and (2) An evaluation of who they are as a person, or "You're no good." Start by explaining that people speak in certain tones for different reasons. For example, a coach who yells at her team might feel frustrated because she knows they can do better. Reinforce the fact that the coach believes in your child (or she wouldn't be on the team), and prompt her to think about how the feedback can be helpful: What if she did apply what they coach is saying? How could her game get even better?
Then, encourage your child to speak with the coach about his comments. She could say something like, "Coach, I know you told me to do X. I am going to focus on applying your advice, do you have any other pointers for me?" Then, after a few practices, she could follow up with the coach, and say, "I've been focusing on incorporating your comments. How do you think I am doing?" This will signal to the coach that her feedback was taken seriously, and she may rethink how she delivers her comments or criticism in the future.
Your strategy: Resist the urge to downplay the situation or your child's feelings. Telling him that it's not that big of a deal will confuse him, because, after all, it is a huge deal to him. And, he may be less likely to discuss these kinds of situations with you in the future. Instead, empathize and validate your child's feelings by saying something along the lines of, "It is OK to feel upset for a bit, then let's figure out what you want to do next." Then, talk him through the situation following these steps:
First, ask your child about situations in the past where he may have acted this way, and why he did it. Bring up instances in which his behavior was forgiven by another friend, or even a family member.
Then, talk about forgiveness -- what it is and what it isn't. For example, forgiveness isn't about letting someone walk all over you. It is about expressing your feelings, and letting the other person know (in a calm way) that his actions are hurtful. Remind your child that it's normal for friends and family to sometimes get upset with each other. You might want to give specific examples of how you worked though a rough patch with a close friend, family member, or partner.
You may also want to help your child rethink and reframe what happened. Maybe the friend is struggling with another situation, and his behavior was unintentional. Instead of thinking "He did this to me," your child may come to realize that his friend was simply focused on himself at the time.
If your child wants to discuss the situation with his friend, help him figure out what he'll say beforehand, and even practice role-playing with you. For example, your child might say something along the lines of, "I was really sad when you didn't invite me to the movies. I thought you were dissing me." Then, encourage him listen to what his friend has to say.
Your strategy: The key here is to help your child reframe her thinking, and talk about her fears in order to overcome them. Consider questions like, What's the worst that could happen? What's the best that could happen? What is likely to happen? This will help her shift away from catastrophic thinking, and hopefully see that there are more possible outcomes than she may realize.
Next, encourage your child to talk about her specific concerns related to trying out. Is she worried that she'll be devastated by not getting the part? That people will laugh? That she will completely freeze up on stage? Then, help her work through those fears. For example, discuss the potential upsides of trying out for the lead and not getting it. Since the teacher knows she's interested in theater, perhaps she'll keep her in mind for future performances, or might give her a different role that she wouldn't have gotten otherwise.
It can also be helpful to remind your child of past situations in which she overcame her insecurities -- whether it involved a social situation like sitting with new friends at lunch, or a school-related one, such as spending extra time on a difficult subject or skill -- and highlight the positive things that happened thanks to her courage.