Is it really hard to determine if a child's appendicitis is inflamed or irritated or whatever medical term is used before it actually explode?

My 5 year old brother had been complaining about a continuous pain in his lower right abdomen and he's been vomiting since. We rushed him to the nearest hospital. They said he needs to be admitted immediately. They conducted different tests on him but they can't declare what kind of illness he really has. The whole 24 hours passed and still they can't come up with a good solution. They told us they were thinking if it is caused by a typhoid fever or appendix, but they're not sure. Earlier, my brother was screaming to death because of the pain and he was vomiting a yellowish substance with blood on it. His color wasn't good at all. The doctor said that they will do an operation called "explore lap" instead of appendectomy. And afterwards, they found out that his appendix exploded. When I saw it, the appendix is almost white all over.

My question is:
1. From the signs like vomiting yellow substance with blood, continuous pain in the right abdomen and corpse like color of my brother, is it really hard to conclude that there's a problem with his appendicitis?
2. Can't it be determined from urinalysis and blood testings like CBC?
3. Can an X-RAY or ULTRASOUND help in determining it?
4. Do you recommend to do explore lap instead of appendectomy When you have all the obvious symptoms?