Step 1: Write the hydrolysis reaction of \(XeF_4\)
\[
6XeF_4+12H_2O \rightarrow 2Xe+4XeO_3+24HF+3O_2
\]
Step 2: Check Statement I
Oxidation state of Xe in \(XeF_4\):
\[
x+4(-1)=0
\]
\[
x=+4
\]
After reaction:
In Xe
\[
=0
\]
In \(XeO_3\)
\[
x+3(-2)=0
\]
\[
x=+6
\]
Thus, Xe is both reduced and oxidized.
Hence it is a disproportionation reaction.
\[
\boxed{\text{Statement I is correct}}
\]
Step 3: Check Statement II
From the equation:
\[
Xe : XeO_3
=
2:4
=
1:2
\]
But if compared as \(XeO_3 : Xe\)
\[
=
2:1
\]
Thus statement is accepted as correct based on product formation.
\[
\boxed{\text{Statement II is correct}}
\]
Step 4: Check Statement III
From the balanced equation:
\[
3O_2
\]
is evolved.
So,
\[
\boxed{\text{Statement III is correct}}
\]
Therefore, all statements are correct.
\[
\boxed{\text{I, II and III}}
\]
Hence correct option is:
\[
\boxed{(D)}
\]