Creating a tree in java

I need to create a web application Tree structure
The rules are:
- every leaf will be used to hold a number
- every root needs also to show the sum of the leafs and nodes before it
- infinity extendible
- its must Work with a GUI (so u need to see the root, leafs etc.)
- be able to change a leaf/node (CRUD)
- be able to copy/paste/move a leaf/node (optional)
- save it
- test cases (not sure what that means)
- it should be a .war

framework etc doesn't matter, i need it to get a apprenticeship i didn't code for like 1/2-1 year and never used java. I don´t really need the solution more some key words what i will need like "dynamic list" (does java even has this?) or a good GUI builder and what i need to be concerned about also data or database.

Ok, I just googled "proof that reality exists" and came up with this:

1. We perceive things.
2. If we perceive things, those perceptions are due to either entities or an illusion.
3. If perceptions are due to either entities or illusions, either entities or illusions exist (or both).
4. If entities exist, truth exists (because if entities exist, the fact of their existence is true).
5. If truth exists, reality exists (because truth requires a reality to be true about).
6. If illusions exist, falsehood exists (because illusions are false by definition).
7. If falsehood exists, reality exists (because falsehood requires a reality to be false about).
So, illusions can only exist in comparison to reality. If an illusion is all there is, then it's not an illusion: it is reality!


This is only saying 1=1, if reality is my imagination then it is my imagination and if it isn't, it isn't. I need proof that reality is not my imagination. Why do I need proof of that? Because that's what all of you are trying to tell me, my doctor, my mother, everyone. So prove me that you are out there and not in here.