"I'll be right there" is different from your other example sentences. When you say "right there", it means that it will be happening quickly. If you are planning to meet a friend, and they are running late, they might say "I'll be right there" when they are quite close. "I'll be there later" implies that there will be a much longer time. "Later" tells us that it won't be so quick. If you are at a party and a friend says "I will be there later", it could be an hour or more. There isn't so much of a rush. "Right there" means the person will be there soon. "Later" means the person will come, but it might not be so soon.