Dear Cristinel,
I congratulate you on your well written essay in which you have clearly pointed out the defects prevailing in Wheeler's views stemming from his delayed choice experiment.
But, your interpretation of Zero Axiom, I feel, is not right. Because you have said that according to Zero Axiom, the proposition p 'and' its negation -p is always true; that is in symbols it is written as (p&-p). But this is wrong, for (p&-p) is 'always' false. So you should say, (p v -p). This proposition is always true for whatever value you ascribe to 'p'. Hence, you better change the last sentence of your essay which reads "Assuming both propositions p and -p are true, we want to prove q. Since p is true, p v q is true. But since -p is true, p is false. From p v q and -p follows that q is true" to "From the proposition (-p or q) is true, we want to prove q. If p is true, q must be true and the whole proposition (-p v q) is true. But if q is false, p must be true"; where 'must' is logical.
In symbolic logic (-p or q) is written as p > q, meaning 'if p then q'.
[p > q, p, * q; p > q, -q, * p] where * means therefore.
Regarding this, please, consult a 'symbolic logician'.
Wishing you best of luck in the contest,
Sreenath